problem solving compare volumes lesson 11 11 answer key

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Go Math Grade 5 Chapter 11 Answer Key Pdf Geometry and Volume

Go Math Grade 5 Chapter 11 Answer Key Pdf: Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume contains the 5th standard solutions with brief explanations which helps the students to gain the highest marks in the exams. This chapter contains the concepts of Geometry and volume of rectangular prisms. We provide the Go Math Grade 5 Answer Key in such a way that the students will never feel difficulty in learning the geometry and volume.

Geometry and Volume Go Math Grade 5 Chapter 11 Answer Key Pdf

Every student has a chance to know how to find out the Geometry and Volume and how to find out the volume of shapes with the Go Math Grade 5 Key. Get quick solutions with Go Math Answer Key. Get the solutions to this chapter topic wise. Go through the topics mentioned below and start your preparation. The concepts in this chapter include polygons, triangles, quadrilaterals, estimate volume, understand volume, the volume of the rectangular prism

Lesson 1: Polygons

Share and Show – Lesson 1: Polygons – Page No. 639

Problem solving – lesson 1: polygons – page no. 640.

Lesson 2: Triangles

Share and Show – Lesson 2: Triangles – Page No. 645

Problem solving – lesson 2: triangles – page no. 646.

Lesson 3: Quadrilaterals

Share and Show – Lesson 3: Quadrilaterals – Page No. 651

Problem solving – lesson 3: quadrilaterals – page no. 652.

Lesson 4: Properties of Two-Dimensional Figures

Share and Show – Lesson 4: Properties of Two-Dimensional Figures – Page No. 455

On your own – lesson 4: properties of two-dimensional figures – page no. 456, share and show – lesson 4: properties of two-dimensional figures – page no. 656, problem solving – lesson 4: properties of two-dimensional figures – page no. 657.

Mid-Chapter Checkpoint

Mid-Chapter Review – Vocabulary – Page No. 661

Mid-chapter review – page no. 662.

Lesson 5: Unit Cubes and Solid Figures

Share and Show – Lesson 5: Unit Cubes and Solid Figures – Page No. 665

Lesson 5: unit cubes and solid figures – page no. 666.

Lesson 6: Understand Volume

Share and Show – Lesson 6: Understand Volume – Page No. 671

Problem solving – lesson 6: understand volume – page no. 672.

Lesson 7: Estimate Volume

Share and Show – Lesson 7: Estimate Volume – Page No. 677

Problem solving – lesson 7: estimate volume – page no. 678.

Lesson 8: Volume of Rectangular Prisms

Share and Show – Lesson 8: Volume of Rectangular Prisms – Page No. 683

Unlock the problem – lesson 8: volume of rectangular prisms – page no. 684.

Lesson 9: Algebra Apply Volume Formulas

Share and Show – Lesson 9: Algebra Apply Volume Formulas – Page No. 689

Problem solving – lesson 9: algebra apply volume formulas – page no. 690.

Lesson 10: Problem Solving Compare Volumes

Share and Show – Lesson 10: Problem Solving Compare Volumes – Page No. 695

On your own – lesson 10: problem solving compare volumes – page no. 696.

Lesson 11: Find Volume of Composed Figures

Share and Show – Lesson 11: Find Volume of Composed Figures – Page No. 701

Problem solving – lesson 11: find volume of composed figures – page no. 702.

Chapter Review/Test

Chapter Review/Test – Page No. 705

Chapter review/test – page no. 706, chapter review/test – page no. 707, chapter review/test – page no. 708, chapter review/test – page no. 709, chapter review/test – page no. 710.

• Chapter Review/Test – Page No. 4910

Chapter Review/Test – Page No. 4920

Chapter review/test – page no. 4930, chapter review/test – page no. 4940.

Answer: Triangle

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of three sides. So, the name of the polygon is a triangle.

Question 1. b. Are all the sides and all the angles congruent? _____

Answer: Yes

Explanation: When line segments have the same length or when angles have the same measure, they are congruent. All sides are equal in the above figure. Thus the above figure is congruent.

Question 1. c. Is the polygon a regular polygon? _____

Explanation: In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above figure is a regular polygon.

Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.

Answer: i. Hexagon ii. Regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 6 sides. So, the name of the polygon is Hexagon. In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above figure is a regular polygon.

Answer: i. Quadrilateral ii. Not regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 4 sides. So, the name of the polygon is Quadrilateral. The above figure doesn’t have the same sides thus the above figure is not a regular polygon.

Answer: i. Octagon ii. Regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 8 sides. So, the name of the polygon is Octagon. In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Octagon is a regular polygon.

Answer: i. Quadrilateral ii. Regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 4 sides. So, the name of the polygon is Quadrilateral. In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Quadrilateral is a regular polygon.

Answer: i. Triangle ii. Not regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of three sides. So, the name of the polygon is a triangle. The above figure doesn’t have the same sides thus the above figure is not a regular polygon.

Answer: i. Heptagon ii. Regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of 7 sides. So, the name of the polygon is Heptagon. In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Heptagon is a regular polygon.

Answer: i. Hexagon ii. Not regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of six sides. So, the name of the polygon is a Hexagon. The above figure doesn’t have the same sides and angles thus the above figure is not a regular polygon.

Answer: i. Pentagon ii. Not regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of five sides. So, the name of the polygon is a pentagon. The above figure doesn’t have the same sides and angles thus the above figure is not a regular polygon.

Answer: i. Pentagon ii. Regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure consists of five sides. So, the name of the polygon is a pentagon. In a regular polygon, all sides are congruent and all angles are congruent. The above figure has the same sides and same angles. Thus the above Pentagon is a regular polygon.

Question 11. Which polygons in the floor plan have four equal sides and four congruent angles? How many of these polygons are there? polygon: __________ The number of polygons: __________

Answer: polygon: Quadrilateral The number of polygons: 8

Explanation: By seeing the above figure we can say that there are eight Quadrilaterals in the octagon. And the number of polygons is 8.

Question 12. Is there a quadrilateral in the floor plan that is not a regular polygon? Name the quadrilateral and tell how many of the quadrilaterals are in the floor plan. Name of quadrilateral: __________ The number of quadrilaterals: __________

Answer: Name of quadrilateral: Trapezoid The number of quadrilaterals: 8

Explanation: The name of the Quadrilateral for the above figure is Trapezoid. There is 8 number of quadrilaterals in the floor plan.

Question 13. Sketch eight points. Then connect the points to draw a closed plane figure. What kind of polygon did you draw? __________

Answer: Octagon

Question 14. Look at the angles for all regular polygons. As the number of sides increases, do the measures of the angles increase or decrease? What pattern do you see? angles measures __________

Answer: Increase

Explanation: As the number of sides increases, the measures of the angles increase. we know that The measure of the interior angle in a regular polygon is equal to x = (n-2)/n(180°) where n is the number of sides of the regular polygon. x is the measure of the interior angle in a regular polygon.

Classify each triangle. Write isosceles, scalene, or equilateral.

Then write acute, obtuse, or right.

Answer: △ – Scalene ∠ – Acute

Explanation: The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. The angles are less than 90° thus the angle is known as an acute angle.

Answer: △ – Equilateral ∠ – Acute

Explanation: The 3 sides of the triangle are equal. If three sides of the triangle are equal it is known as the equilateral triangle. The angles are less than 90° thus the angle is known as an acute angle.

△ – Isosceles ∠ – Acute

Explanation: The 2 sides of the triangle are equal and the third side is not equal. If two sides of the triangle are different it is known as Isosceles. The angles are less than 90° thus the angle is known as an acute angle.

On Your Own

Answer: △ – Scalene ∠ – Right

Explanation: The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. One of the angle is 90° thus the angle is known as a right angle.

Answer: △ – Isosceles ∠ – Acute

Answer: △ – Scalene ∠ – Obtuse

Explanation: The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. The angles are more than 90° thus the angle is known as an obtuse angle.

A triangle has sides with the lengths and angle measures given.

Question 7. sides: 3.5 cm, 6.2 cm, 3.5 cm angles: 27°, 126°, 27° △ __________ ∠ __________

Answer: △ – Isosceles ∠ – Obtuse

Explanation: The 2 sides of the triangle are equal and the third side is not equal. If two sides of the triangle are different it is known as Isosceles. One of the angle is more than 90° thus the angle is known as an obtuse angle.

Question 8. sides: 2 in., 5 in., 3.8 in. angles: 43°, 116°, 21° △ __________ ∠ __________

Explanation: The 3 sides of the triangle are unequal. If three sides of the triangle are different it is known as Scalene. One of the angle is more than 90° thus the angle is known as an obtuse angle.

Question 10. Draw 2 equilateral triangles that are congruent and share a side. What polygon is formed? Is it a regular polygon? What polygon is formed? __________ Is it a regular polygon? __________

Answer: The name for the polygon is Quadrilateral. In a regular polygon, all sides are congruent and all angles are congruent.

Question 11. What’s the Error? Shannon said that a triangle with exactly 2 congruent sides and an obtuse angle is an equilateral obtuse triangle. Describe her error. Type below: __________

Answer: All angles of an equilateral triangle are acute. You cannot have an obtuse angle in an equilateral angle. And all of the angles must be congruent.

Question 12. Test Prep Which kind of triangle has exactly 2 congruent sides? Options: a. isosceles b. equilateral c. scalene d. right

Answer: isosceles

Explanation: An isosceles triangle, therefore, has both two equal sides and two equal angles. Thus the correct answer is option A.

Classify the triangles in the structures below. Write isosceles, scalene, or equilateral. Then write acute, obtuse, or right.

Answer: △ – Equilateral triangle ∠ – Acute

Explanation: From the figure, we can see an equilateral triangle. In an equilateral triangle, all sides will be less than 90°. So it is an acute angle.

Answer: △ – Scalene triangle ∠ – Right

Explanation: In the above figure, we can see a right-angle triangle. The three sides of the above triangle is different. So, it is known as the scalene triangle.

Explanation: The above figure consists of same sides. Thus the above Quadrilateral is congruent.

Question 1. b. How many right angles, if any, does the quadrilateral have? _____

The above figure doesn’t have any straight line. Thus the above figure has 0 right angles.

Question 1. c. How many pairs of parallel sides, if any, does the quadrilateral have? _____ pairs

Explanation: The above has two parallel sides. Yes, the Quadrilateral has the parallel sides.

Question 1. So, quadrilateral ABCD is a ______________ . _________

Answer: Parallelogram

Explanation: A parallelogram is a special trapezoid with opposite sides are equal.

Classify the quadrilateral in as many ways as possible.

Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid.

Answer: The possible ways of Quadrilateral are: 1. Rectangle 2. Parallelogram 3. Quadrilateral

Answer: The possible ways of Quadrilateral are: 1. Quadrilateral 2. Trapezoid

Answer: The possible ways of Quadrilateral for the above figure are: 1. Square 2. Quadrilateral 3. Parallelogram 4. Rectangle 5. Rhombus

Answer: The possible ways of Quadrilateral for the above figure are: 1. Trapezoid 2. Parallelogram

Answer: The possible ways of Quadrilateral for the above figure are: 1. Rhombus 2. Parallelogram 3. Square

Answer: The possible ways of Quadrilateral for the above figure are: 1. Rectangle 2. Parallelogram

Solve the problems.

Question 8. A quadrilateral has exactly 2 congruent sides. Which quadrilateral types could it be? Which quadrilaterals could it not be? Type below: _________

Answer: A rectangle has 2 congruent sides.

Explanation: The type of quadrilateral that has two congruent sides is a rectangle.

Question 9. What’s the Error? A quadrilateral has exactly 3 congruent sides. Davis claims that the figure must be a rectangle. Why is his claim incorrect? Use a diagram to explain your answer. Type below: _________

Answer: Daviss’s claim is incorrect because a rectangle does not have three congruent sides.

Go Math Grade 5 Lesson 11.3 Homework Answers Question 10. The opposite corners of a quadrilateral are right angles. The quadrilateral is not a rhombus. What kind of quadrilateral is this figure? Explain how you know. Type below: _________

Question 11. I am a figure with four sides. I can be placed in the following categories: quadrilateral, parallelogram, rectangle, rhombus, and square. Draw me. Explain why I fit into each category. Type below: _________

Question 12. Test Prep A quadrilateral has exactly 1 pair of parallel sides and no congruent sides. What type of quadrilateral is it? Options: a. rectangle b. rhombus c. parallelogram d. trapezoid

Answer: Trapezoid

Explanation: A quadrilateral with one pair of parallel sides is a trapezoid. Thus the correct answer is option D.

Question 1. Then, fold the triangle to match each pair of sides to determine if at least two of the sides are congruent. As you test the sides, record or draw the results for each pair to make sure that you have checked all pairs of sides. Possible drawings are shown. Type below: _________

Question 1. Finally, answer the question. ______

Question 2. What if Erica also wants to show, without using a protractor, that the triangle has one right angle and two acute angles? Explain how she can show this.

Answer: The sum of three angles = 180 If one of the angles is 90 then the other two angles will be acute angles.

Question 3. December, January, and February were the coldest months in Kristen’s town last year. February was the warmest of these months. December was not the coldest. What is the order of these months from coldest to warmest? Coldest: _________ _________ Warmest: _________ _________

Answer: Coldest: January December Warmest: February

Explanation: January and December are the coldest months of the year depending on the direction of the wind. February is the warmest month among these months.

Question 4. Jan enters a 20-foot by 30-foot rectangular room. The long sides face north and south. Jan enters the exact center of the south side and walks 10 feet north. Then she walks 8 feet east. How far is she from the east side of the room? ______ ft

Answer: 7 feet

Explanation: Given that, Jan enters a 20-foot by 30-foot rectangular room. The long sides face north and south. Jan enters the exact center of the south side and walks 10 feet north. Then she walks 8 feet east. Jan is 7 feet from the east wall in the room.

Answer: 3 lines

Explanation: From the above figure, we can see that there are 18 congruent squares. To find the least number of lines Max can draw we have to divide the number of squares by the number of congruent rectangles 18 ÷ 6 = 3 Thus the least number of lines that Max can Draw is 3 lines.

Geometry Chapter 11 Test Answer Key Go Math Grade 5 Workbook Question 6. Of the 95 fifth and sixth graders going on a field trip, there are 27 more fifth graders than sixth graders. How many fifth graders are going on the field trip? 5th graders = ______

Explanation: Since we are not told how many 6th graders are going on the trip let’s use a variable, the letter x. Now let’s understand the problem in the “math” language. x= the number of 6th graders. X+27= the number of 5th graders since there are 27 more fifth-graders than sixth graders. x+x+27 = 95 2x+27=95 -27 -27 2x+ 0 =68 2x=68 divide by 2 on both sides. x = 34 Now, remember how x+27 = the number of 5th graders going on the trip? Since we know that x=34, substitute the x as 34+27 which = 61 fifth graders going on the trip.

Question 7. Sam’s paper route begins and ends at the corner of Redwood Avenue and Oak Street. His route is made up of 4 streets, and he makes no 90° turns. What kind of polygon do the streets of Sam’s paper route form? Name the streets in Sam’s route. _________

Explanation: Given that, Sam’s paper route begins and ends at the corner of Redwood Avenue and Oak Street. His route is made up of 4 streets, and he makes no 90° turns. By following the route map we can say that the polygon is a parallelogram.

Question 8. Sam’s paper route includes all 32 houses on two pairs of parallel streets. If each street has the same number of houses, how many houses are on each street? Name the parallel streets. ______ houses on each street

Explanation: Given, Sam’s paper route includes all 32 houses on two pairs of parallel streets. If each street has same number of houses we have to divide 32 by 4 32 ÷ 4 = 8 Thus there are 8 houses on each street.

Explanation: A square is a type of quadrilateral that has opposite sides that are congruent and parallel. Thus the correct answer is option B.

Classify the solid figure. Write prism, pyramid, cone, cylinder, or sphere.

Answer: Triangular prism

Explanation: A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise, it is oblique.

Answer: Sphere

Explanation: A sphere has no bases and 1 curved surface.

Answer: Hexagonal Base Pyramid

Explanation: A pyramid that has a hexagonal base, that is, a base with six sides and 6 triangular lateral faces, then it is a hexagonal pyramid.

Answer: Pentagonal prism

Explanation: A pentagonal prism is a prism that has two pentagonal bases top and bottom and five rectangular sides. It is a type of heptahedron with 7 faces, 10 vertices, and 15 edges.

Answer: Pentagonal Base Pyramid

Explanation: In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point.

Answer: Cylinder

Explanation: A cylinder has 2 congruent circular bases and 1 curved surface.

Answer: Rectangular prism

Explanation: A rectangular prism is a polyhedron with two congruent and parallel bases. It is also a cuboid. It has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

Answer: Cone

Explanation: A cone has 1 circular base and 1 curved surface.

Answer: Triangle base pyramid

Explanation: A triangle-based pyramid has four triangular sides. The base can be any shape or size of the triangle but usually, it is an equilateral triangle. This means the three sides of the pyramid are the same size as each other and the pyramid looks the same if you rotate it.

Explanation: A prism’s base shape is used to name the solid figure. The base shape of this prism is a triangle. The prism is a triangular prism.

Answer: Hexagonal Prism

Explanation: In geometry, the hexagonal prism is a prism with a hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces.

Answer: Square Pyramid

Explanation: In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid and has symmetry. If all edges are equal, it is an equilateral square pyramid.

Answer: Octogonal Prism

Explanation: In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps. If the faces are all regular, it is a semiregular polyhedron.

Question 16. Mario is making a sculpture out of stone. He starts by carving a base with five sides. He then carves five triangular lateral faces that all meet at a point at the top. What three-dimensional figure does Mario make? _________

Answer: Pentagonal Pyramid

Explanation: Given, Mario is making a sculpture out of stone. He starts by carving a base with five sides. He then carves five triangular lateral faces that all meet at a point at the top. The polygon which has 5 sides is a pentagon. The three-dimensional figure which meets at the same point is the pyramid. The 3-dimensional figure that Mario makes is Pentagonal Pyramid So, the answer to the above question is Pentagonal Pyramid.

Question 17. What is another name for a cube? Explain your reasoning. Type below: _________

Answer: The cube can also be called a regular hexahedron. It is one of the five regular polyhedrons, which are also sometimes referred to as the Platonic solids.

Connect to Reading

Example Read the description. Underline the details you need to identify the solid figure that will name the correct building.

Identify the solid figure and name the correct building.

Question 18. Solve the problem in the Example. Solid figure: _________ Building: _________

Answer: i. Pyramid ii. Luxor Hotel-Las Vegas-Nevada

Explanation: The 3rd figure is in the form of a pyramid. The name of the pyramid-shaped building is Luxor Hotel Las Vegas-Nevada.

Go Math Grade 5 Chapter 11 Answer Key Pdf Question 19. This building was completed in 1902. It has a triangular foundation and a triangular roof that are the same size and shape. The three sides of the building are rectangles. Solid figure: _________ Building: _________

Answer: i. prism ii. Flatiron Building-New York City-New York

Explanation: The triangle-shaped figure is in the form of a prism. The name of the triangular prism building is Flatiron Building-New York, New York.

Question 1. A closed plane figure with all sides congruent and all angles congruent is called a ________ . _________

Answer: Regular Polygon

Question 2. Line segments that have the same length or angles that have the same measure are __________ . _________

Answer: Congruent

Concepts and Skills

Answer: i. Hexagon ii. Regular Polygon

Answer: i. Triangle ii. Non-Regular

Answer: i. Pentagon ii. Not Regular

Answer: i. Equilateral ii. Acute

Answer: i. Isosceles ii. Right

Answer: i. Isosceles ii. Obtuse

Classify the quadrilateral in as many ways as possible. Write quadrilateral, parallelogram, rectangle, rhombus, square, or trapezoid.

Answer: 1. Quadrilateral 2. Trapezoid

Answer: 1. Quadrilateral 2. Parallelogram 3. Rectangle

Answer: 1. Quadrilateral 2. Parallelogram 3. Rhombus 4. Rectangle 5. Square

Fill in the bubble completely to show your answer.

Answer: right isosceles

Explanation: The above figure is a right angle and the two sides of the triangle are equal. The above figure is a right isosceles. Thus the correct answer is option A.

Answer: quadrilateral, parallelogram, rhombus, rectangle, square

Explanation: The 3-dimensional figure of the above rectangle is a rectangular prism. Thus the correct answer is option C.

Count the number of cubes used to build each solid figure.

Explanation: By seeing the above figure we can say that the rectangular prism has 3 unit cubes.

Explanation: The above figure shows that there are 5 congruent squares of 3 lines. 5 × 3 = 15 unit cubes

Explanation: The above figure shows that there are 4 congruent squares of 3 lines. 4 × 3 = 12 unit cubes

Explanation: The above figure shows that there are 6 congruent squares of 2 lines. 6 × 2 = 12

Explanation: By seeing the above figure we can say that there are 5 unit cubes.

Explanation: There are 6 congruent squares in the above figure.

Explanation: The figure shows that there are 7 unit cubes.

Question 8. How are the rectangular prisms in Exercises 3–4 related? Can you show a different rectangular prism with the same relationship? Explain. Type below: _________

Compare the number of unit cubes in each solid figure. Use < , > or =.

Use the information to answer the questions.

Question 11. There are 38 Cube Houses. Each house could hold 1,000 unit cubes that are 1 meter by 1 meter by 1 meter. Describe the dimensions of a cube house using unit cubes. Remember that the edges of a cube are all the same length. Each dimension = ______ meters

Answer: 10 meters

Explanation: So each house can hold 1000 cubes that are 1 meter in length. The house is also shaped like a cube, so you need to cube-root 1000. The cube root of 1000 is 10. So the cube house has a length, width, and height of 10 meters. V = lbh V = 10 m × 10 m × 10 m = 1000 cu. meter Thus Each dimension is 10 meters.

Understanding Volume 5th Grade Geometry Answers Question 12. The Nakagin Capsule Tower has 140 modules and is 14 stories high. If all of the modules were divided evenly among the number of stories, how many modules would be on each floor? How many different rectangular prisms could be made from that number? Type below: _________

Answer: 10 modules on each floor

Explanation: The Nakagin Capsule Tower has 140 modules and is 14 stories high. Divide 140 modules by 14 140 ÷ 14 = 10 Thus 10 modules would be on each floor. The factors of 10 are 1, 2, 5. 1 × 10 = 10 2 × 5 = 10 Thus 2 different rectangular prisms can be made from 10 unit cubes.

Use the unit given. Find the volume.

Answer: 48 cu. cm

Explanation: Given that, L = 4cm B = 4cm H = 3 cm We know that, The volume of the cuboid is lbh V = 4 cm × 4 cm × 3 cm = 48 cubic cm Thus the volume for the above cube is 48 cubic cm.

Answer: 24 cu. in.

Explanation: Given that, L = 3 in B = 2 in H = 4 in. We know that, The volume of the cuboid is lb V = 3 in × 2 in × 4 in = 24 cubic inches Therefore the volume for the above cube is 24 cubic inches.

Answer: 36 cu. ft

Explanation: Given that, L = 6 ft B = 2 ft H = 3 ft We know that, The volume of the cuboid is lbh V = 6 ft × 2 ft × 3 ft = 36 cubic feet V = 36 cu. ft Therefore the volume for the above figure is 36 cu. ft

Answer: 60 cu. in

Given that, L = 5 in. B = 4 in. H = 3 in. We know that, The volume of the cuboid is lbh V = 5 in × 4 in × 3 in = 60 cubic inches Thus the volume for the above figure is 60 cu. in.

Compare the volumes. Write < , >, or =.

Question 7. What’s the Error? Jerry says that a cube with edges that measure 10 centimeters has a volume that is twice as much as a cube with sides that measure 5 centimeters. Explain and correct Jerry’s error. Type below: __________

Answer: Let v1 equal the 10 cm sided cube’s volume. Let v2 equal the 5 cm sided cube’s volume. v1 = 10 × 10 10 = 1000 cu. cm v2 = 5 × 5 × 5 = 125 cu. cm To find the relationship between the two volumes, divide the first volume by the second. r = v1 ÷ v2 r = 1000 ÷ 125 = 8 The volume differ by a factor of 8. Thus the volume differs by a factor of 8, not by a factor of 2.

Question 8. Pattie built a rectangular prism with cubes. The base of her prism has 12 centimeter cubes. If the prism was built with 108 centimeter cubes, how many layers does her prism have? What is the height of her prism? layers: ______ the height of the prism: ______ cm

Answer: 9 layers, the height of the prism is 9 cm

Explanation: Given: Pattie built a rectangular prism with cubes. The base of her prism has 12-centimeter cubes. The prism was built with 108 cm cubes. To find the layers divide the number of cubes by base of the prism That means 108 ÷ 12 108/12 = 9 Thus the prism has 9 layers. Now we have to find the base of the prism 108 = b × h 12 × h = 108 h = 108/12 = 9 Therefore the height of the prism = 9 cm

Question 9. A packing company makes boxes with edges each measuring 3 feet. What is the volume of the boxes? If 10 boxes are put in a larger, rectangular shipping container and completely fill it with no gaps or overlaps, what is the volume of the shipping container? volume of the boxes: __________ cu ft volume of the shipping container = __________ cu ft

Answer: the volume of the boxes: 27 cu ft the volume of the shipping container = 27 cu ft

Explanation: A packing company makes boxes with edges each measuring 3 feet. Volume of the cube = lbh V = 3 × 3 × 3 = 27 cubic feet Thus the volume of the boxes is 27 feet. The volume of the boxes for 10 boxes is 27 × 10 = 270 cubic feet Therefore the volume of the shipping container is 27 cu ft

Answer: 75 cubic centimeters

Explanation: L = 5 cm B = 3 cm H = 5 cm Volume of the rectangular prism is lbh V = 5 cm × 3 cm × 5 cm = 75 cubic centimeter V = 75 cu. cm Thus the correct answer is option D.

Estimate the volume.

Answer: Given that the volume of each box is 125 cubic inches. By seeing the above figure we can say that there are 9 boxes in the larger box. Thus there are 9 tissue boxes in the larger box. Now to find the volume of the tissue boxes. We have to multiply the number of boxes with the volume of the box V = 125 × 9 = 1125 cubic inches. Therefore The estimated volume of the box holding the tissue boxes is 1125 cubic inches.

Answer: Given that, the volume of the chalk box is 16 cubic inches. From the figure, we can see that there are 24 boxes. The volume of the large box is 24 × 16 = 384 cubic inches. Therefore the estimated volume of the large box is 384 cu in.

Answer: Given, the volume of the small jewelry box is 30 cu cm There are 10 small jewelry boxes. V = 30 × 10 = 300 cu. cm Thus the estimated volume of large box is 300 cu. cm

Answer: Given that, the volume of the book is 80 cu. in There are 12 books in the figure. Multiply the number of books with the volume of each book = 12 × 80 = 960 cu. inches Thus the estimated volume of large books is 960 cu in.

Answer: Volume of spaghetti box is 750 cu. cm Volume = 2 × 5 × 4 = 40 Number of boxes = 40 Now multiply 40 with 750 cu. cm to find the volume of large box V = 40 × 750 cu. cm V = 30000 cubic cm Therefore the estimated Volume of large box is 30000 cubic cm

Answer: Given the volume of a cereal box is 324 cu. in Number of boxes is 2 × 3 × 3 = 18 The volume of large box is 18 × 324 cu. in V = 18 × 324 cu. in = 5832 cubic inches Thus the estimated Volume of large box is 5832 cubic inches.

Answer: Volume of pencil box is 4500 cu cm Number of pencil boxes = 2 × 5 = 10 The volume of large box is 4500 × 10 = 45000 cu cm Thus the estimated volume of large box is 45000 cu cm

Sense or Nonsense?

Answer: Calculate the books in box 1 V = lbh V1 = 2 × 4 × 7 = 56 books Calculate the volume of books in box 2 V = lbh V2 = 1 × 4 × 14 = 56 books So, both boxes hold the same number of books. Thus Marcelle’s statement make sense.

Find the volume.

Answer: 120 cu. in

Explanation: From the figure, we can say that the length of the rectangular prism is 4 in The width of the rectangular prism is 5 in The height of the rectangular prism is 6 in. The volume of the rectangular prism is l × w × h V = 4 in × 6 in × 5 in = 120 cu. in So, the volume of the prism is 120 cu. in

Explanation: From the figure, we can say that the length of the rectangular prism is 2 cm The width of the rectangular prism is 3 cm The height of the rectangular prism is 3 cm The volume of the rectangular prism is l × w × h V = 2 cm × 3 cm × 3 cm = 18 cu. cm Thus the volume of the rectangular prism is 18 cu. cm

Explanation: From the figure, we can say that the length of the rectangular prism is 2 in. The width of the rectangular prism is 6 in. The height of the rectangular prism is 1 in. The volume of the rectangular prism is l × w × h V = 2 in × 6 in × 1 in V = 12 Cu in. Thus the volume of the rectangular prism is 12 Cu in.

Explanation: From the figure, we can say that the length of the rectangular prism is 1 mm The width of the rectangular prism is 8 mm The height of the rectangular prism is 3 mm The volume of the rectangular prism is l × w × h V = 1 mm × 8 mm × 3 mm V = 24 Cu. mm Thus the volume of the rectangular prism is 24 Cu. mm

Answer: 160

Explanation: From the figure, we can say that the length of the rectangular prism is 10 cm The width of the rectangular prism is 4 cm The height of the rectangular prism is 4 cm The volume of the rectangular prism is l × w × h V = 10 cm × 4 cm × 4 cm = 160 Cu. cm Thus the volume of the rectangular prism is 160 Cu. cm

Answer: 150

Explanation: From the figure, we can say that the length of the rectangular prism is 5 ft The width of the rectangular prism is 6 ft The height of the rectangular prism is 5 ft The volume of the rectangular prism is l × w × h V = 5 ft × 6 ft × 5 ft V = 150 Cu. ft Thus the volume of the rectangular prism is 150 Cu. ft

Answer: 196

Explanation: From the figure, we can say that the length of the rectangular prism is 7 in. The width of the rectangular prism is 7 in. The height of the rectangular prism is 4 in. The volume of the rectangular prism is l × w × h V = 7 in × 7 in × 4 in = 196 Cu. in Thus the volume of the rectangular prism is 196 Cu. in

Answer: We need to find the volume of the travel crate that Rich should build.

Question 8. b. How can you use Thomas’s size to help you solve the problem? Type below: _________

Answer: Thomas’s size helps to find the length, width and height of the dog crate.

Question 8. c. What steps can you use to find the size of Thomas’s crate? Type below: _________

Answer: Rich is building a travel crate for his dog, Thomas, a beagle mix who is about 30 inches long, 12 inches wide, and 24 inches tall. For Thomas to travel safely, his crate needs to be a rectangular prism that is about 12 inches greater than his length and width, and 6 inches greater than his height. Length of the dog crate is 30 in + 12 in = 42 inches Width of the dog crate is 12 inches more than width of Thomas crate = 12 in + 12 in = 24 inches Height of the dog crate is 24 in + 6 in = 30 inches V = 42 in × 24 in × 30 in V = 30,240 cu in

Question 8. d. Fill in the blanks for the dimensions of the dog crate. length: _____ width: _____ height: _____ area of base: _____ Type below: _________

Answer: Crate length = 30 + 12 = 42 in Crate width = 12 + 12 = 24 in Crate height = 24 + 6 = 30 in Area of base = l × w A = 42 in × 24 in = 1008 sq in.

Question 8. e. Find the volume of the crate by multiplying the base area and the height. ______ × ______ = ______ So, Rich should build a travel crate for Thomas that has a volume of ______ . Type below: _________

Answer: Area of base = l × w A = 42 in × 24 in = 1008 sq in. Height = 30 in V = 1008 sq in × 30 in = 30240 cu. in So, Rich should build a travel crate for Thomas that has a volume of 30240 cu. in

Answer: 175 in. 3

Explanation: Length = 5 in Width = 7 in Height = 5 in Volume of the rectangular prism is l × w × h V = 5 in × 7 in × 5 in V = 175 in. 3 The volume of the rectangular prism is 175 in. 3 Therefore the correct answer is option D.

Explanation: length = 2 ft width = 4 ft height = 5 ft Volume of the rectangular prism is l × w × h V = 2 ft × 4 ft × 5 ft V = 40 cu ft Volume of the rectangular prism is 40 cu. ft

Answer: 144

Explanation: length = 4 cm width = 4 cm height = 9 cm Volume of the rectangular prism is l × w × h V = 4 cm × 4 cm × 9 cm V = 144 cu cm Volume of the rectangular prism is 144 cu cm

Answer: 216

Explanation: length = 6 in width = 6 in height = 6 in Volume of the prism is l × w × h V = 6 in × 6 in × 6 in V = 216 cu. in Thus the Volume of the prism is 216 cu. in.

Answer: 192

Explanation: length = 12 ft width = 4 ft height = 4 ft Volume of the rectangular prism is l × w × h V = 12 ft × 4 ft × 4 ft V = 192 cu ft Therefore, the Volume of the rectangular prism is 192 cu ft.

Answer: 240

Explanation: length = 10 cm width = 6 cm height = 4 cm Volume of the rectangular prism is l × w × h V = 10 cm × 6 cm × 4 cm V = 240 Cu. cm Therefore, the Volume of the rectangular prism is 240 Cu. cm.

Answer: 1008

Explanation: length = 14 in. width = 6 in. height = 12 in. Volume of the rectangular prism is l × w × h V = 14 in × 6 in × 12 in V = 1008 cu. in Thus the Volume of the rectangular prism is 1008 cu. in

Explanation: length = 7 ft width = 6 ft height = ■ ft Volume of the rectangular prism is l × w × h 420 cu ft = 7 ft × 6 ft × ■ ■ × 42 sq ft = 420 cu ft ■ = 420 cu ft ÷ 42 sq ft ■ = 10 ft

Explanation: length = 6 cm width = 15 cm height = ■ cm Volume of the rectangular prism is l × w × h V = 900 cu cm 900 cu cm = 6 cm × 15 cm × ■ cm 900 cu cm = 90 sq cm × ■ cm ■ cm = 900 cu cm ÷ 90 sq cm ■ cm = 10 cm

Answer: 40 cu ft of water

Explanation: The Jade Restaurant has a large aquarium on display in its lobby. The base of the aquarium is 5 feet by 2 feet. The height of the aquarium is 4 feet. Volume = b × w × h V = 5 feet × 2 feet× 4 feet V = 40 Cu. ft Therefore, the volume of the aquarium is 40 cu ft of water.

Question 10. The Pearl Restaurant put a larger aquarium in its lobby. The base of their aquarium is 6 feet by 3 feet, and the height is 4 feet. How many more cubic feet of water does the Pearl Restaurant’s aquarium hold than the Jade Restaurant’s aquarium? ____ cu ft

Answer: 32 cu ft

Explanation: The Pearl Restaurant put a larger aquarium in its lobby. The base of their aquarium is 6 feet by 3 feet, and the height is 4 feet. Volume = b × w × h V = 6 feet × 3 feet × 4 feet = 72 cu. feet Thus the Volume of Pearl Restaurant’s aquarium is 72 cu. feet The volume of the Jade Restaurant’s aquarium is 40 cu ft of water V = Vp – Vj V = 72 – 40 = 32 cu feet

Question 11. Eddie measured his aquarium using a small fish food box. The box has a base area of 6 inches and a height of 4 inches. Eddie found that the volume of his aquarium is 3,456 cubic inches. How many boxes of fish food could fit in the aquarium? Explain your answer. ____ boxes

Answer: 144 boxes

Explanation: Volume = b × h V = 6 in × 4 in = 24 cu in To find out how many boxes will fit, divide the aquarium volume by the food box volume. numfit = Vaq/Vbox numfit = 3456/24 = 144 144 fish food boxes fir inside the aquarium.

Question 12. Describe the difference between area and volume. Type below: _________

Answer: The surface area is the sum of the areas of all the faces of the solid figure. It is measured in square units. Volume is the number of cubic units that make up a solid figure.

Answer: 1,050 cubic centimeters

Explanation: L = 15 cm W = 10 cm H = 7 cm V = lwh V = 15 cm × 10 cm × 7 cm = 1050 cubic centimeters Thus the correct answer is option C.

Question 1. Mr. Price makes cakes for special occasions. His most popular-sized cakes have a volume of 360 cubic inches. The cakes have a height, or thickness, of 3 inches, and have different whole number lengths and widths. No cakes have a length or width of 1 or 2 inches. How many different cakes, each with a different-size base, have a volume of 360 cubic inches? First, think about what the problem is asking you to solve, and the information that you are given. Next, make a table using the information from problem. Finally, use the table to solve the problem. Type below: _________

Answer: There are total of 8 different possible combination of length and width

Explanation: Volume = 360 cubic inches Height = 3 inches Volume = l x w x h 360 = l x w x 3 l x w = 120 The factors of 120 are, 1 x 120, 2x 60, 3 x 40, 4 x 30, 5 x 24, 6 x 20, 8 x 15, 10 x 12

Question 2. What if the 360 cubic-inch cakes are 4 inches thick and any whole number length and width are possible? How many different cakes could be made? Suppose that the cost of a cake that size is $25, plus $1.99 for every 4 cubic inches of cake. How much would the cake cost? Type below: _________

Answer: Since the store have a volume of 360 cu in and a height of 4 in. We need to find the number of different stones which have a base of 90 sq in. V = b × h B = 360 cu in/4 in B = 90 sq in. Consider the factors of 90. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 Make a table with the base, height and volume for each pair of factors Height = 4 in 1 × 90 × 4 = 360 cu in 2 × 45 × 4 = 360 cu in 3 × 30 × 4 = 360 cu in 5 × 18 × 4 = 360 cu in 6 × 15 × 4 = 360 cu in 9 × 10 × 4 = 360 cu in 6 different sized paving stones. Remember that each store has a volume of 360 cu in. Divide by 4 to find how many 4 cu in per stone Concrete = $0.18 × (360/4) = $0.18 × 90 = $18.70 The cost of the stone plus the concrete cost = $2.50 + concrete Cost = $2.50 + $16.20 = $18.70

Question 3. One company makes inflatable swimming pools that come in four sizes of rectangular prisms. The length of each pool is twice the width and twice the depth. The depth of the pools are each a whole number from 2 to 5 feet. If the pools are filled all the way to the top, what is the volume of each pool? Type below: _________

Answer: If the depth of the pool is 2 feet then the length of the pool is twice the width and twice the depth That means 2 feet × 2 × 2 = 8 feet Width is twice the depth W = 2 feet × 2 = 4 feet The volume of the rectangular swimming pool is l × w × h V = 8 ft × 4 feet × 2 ft V = 64 cu ft If the depth of the pool is 3 feet then the length of the pool is twice the width and twice the depth That means 3 feet × 2 × 2 = 12 feet Width is twice the depth W = 3 feet × 2 = 6 feet The volume of the rectangular swimming pool is l × w × h V = 12 ft × 6 feet × 2 ft V = 144 cu ft If the depth of the pool is 4 feet then the length of the pool is twice the width and twice the depth That means 4 feet × 2 × 2 = 16 feet Width is twice the depth W = 4 feet × 2 = 8 feet The volume of the rectangular swimming pool is l × w × h V = 16 ft × 8 feet × 2 ft V = 256 cu ft If the depth of the pool is 5 feet then the length of the pool is twice the width and twice the depth That means 5 feet × 2 × 2 = 20 feet Width is twice the depth W = 5 feet × 2 = 10 feet The volume of the rectangular swimming pool is l × w × h V = 20 ft × 10 feet × 2 ft V = 400 cu ft

Question 4. Ray wants to buy the larger of two aquariums. One aquarium has a base that is 20 inches by 20 inches and a height that is 18 inches. The other aquarium has a base that is 40 inches by 12 inches and a height that is 12 inches. Which aquarium has a greater volume? By how much? Type below: _________

Answer: 1440 cu. in

Explanation: Volume = l × w × h Volume of Aquarium 1 = 20 in × 20 in × 18 in V = 7200 cu. in Volume = l × w × h Volume of Aquarium 2 is 40 in × 12 in × 12 in V for A2 = 5760 cu in A1 > A2 A1 has a greater volume. Subtract A2 from A1 A1 – A2 = 7200 cu in – 5760 cu in = 1440 cu in The volume of Aquarium 1 is 1440 cu in more than Volume of Aquarium 2.

Question 5. Ken owns 13 CDs. His brother Keith has 7 more CDs than he does. Their brother, George, has more CDs than either of the younger brothers. Together, the three brothers have 58 CDs. How many CDs does George have? ______ CDs

Answer: 25 CDs

Explanation: Given that, Ken owns 13 CDs. His brother Keith has 7 more CDs than he does. Their brother, George, has more CDs than either of the younger brothers. Together, the three brothers have 58 CDs. Keith has 7 more CDs than Ken That means he has 7 + 13 = 20 CDs Now subtract Ken’s CDs, Keith CDs from the total number of CDs. = 58 – 20 – 13 = 25 CDs. Thus George has 25 CDs.

Question 6. Kathy has ribbons that have lengths of 7 inches, 10 inches, and 12 inches. Explain how she can use these ribbons to measure a length of 15 inches. Type below: _________

Answer: She could take the 10-inch ribbon and then use 5 inches from the 7-inch ribbon

Question 7. A park has a rectangular playground area that has a length of 66 feet and a width of 42 feet. The park department has 75 yards of fencing material. Is there enough fencing material to enclose the playground area? Explain. ______

Explanation: A park has a rectangular playground area that has a length of 66 feet and a width of 42 feet. The park department has 75 yards of fencing material. Area of the rectangular playground = l × w A = 66 feet × 42 feet A = 2772 sq. ft Perimeter of the rectangular playground = 2l + 2w P = 2 × 66 + 2 × 42 P = 216 ft Now convert from feet to yard We know that 1 yard = 3 feet 216 ft = 1/3 × 216 = 72 yard 72 yard is less than 75 yard Thus the park department has enough fencing material.

Question 8. Test Prep John is making a chest that will have a volume of 1,200 cubic inches. The length is 20 inches and the width is 12 inches. How many inches tall will his chest be? Options: a. 4 in. b. 5 in. c. 6 in. d. 7 in.

Answer: 5 in

Explanation: John is making a chest that will have a volume of 1,200 cubic inches. The length is 20 inches and the width is 12 inches. Volume = l × w × h 1200 cu in = 20 in × 12 in × h 240 sq in × h = 1200 cu in h = 1200 cu in ÷ 240 sq in h = 5 in Thus John’s chest will be 5 inches tall. The correct answer is option B.

Find the volume of the composite figure.

Answer: 88 cu in.

Explanation: Split the figure into 2 parts Volume of figure 1: b = 2 in h = 3 in w = 4 in V = 2 in × 4 in × 3 in V = 24 cu. in Volume of figure 2: b = 8 in w = 4 in h = 2 in V = 8 in × 4 in × 2 in V = 64 in Volume of the composite figure = 24 cu in + 64 cu. in = 88 cu. in

Answer: 48 cu cm

Explanation: Split the figure into 2 parts Volume of figure 1: b = 3 cm h = 1 cm w = 2 cm V = 3 cm × 2 cm × 1 cm V = 6 cu. cm Volume of figure 2: b = 7 cm w = 6 cm h = 1 cm V = 7 cm × 6 cm × 1 cm V = 42 cu. cm Volume of the composite figure = 42 cu. cm + 6 cu. cm = 48 cu cm

Answer: 52 cu ft

Explanation: Split the figure into 2 parts Volume of figure 1: b = 6 ft h = 2 ft w = 3 ft V = 6 ft × 3 ft × 2 ft V = 36 cu. ft Volume of figure 2: b = 4 ft w = 2 ft h = 2 ft V = 4 ft × 2 ft × 2 ft V = 16 cu. ft Volume of the composite figure = 36 cu. ft + 16 cu. ft = 52 cu ft

Answer: 108 cu. cm

Explanation: Split the figure into 2 parts Volume of figure 1: b = 3 cm w = 8 cm h = 2 cm V = 3 cm × 8 cm × 2 cm V = 48 cu cm Volume of figure 2: b = 10 cm w = 3 cm h = 2 cm V = 10 cm × 3 cm × 2 cm V = 60 cu cm Volume of the composite figure = 48 cu cm + 60 cu cm = 108 cu. cm

Answer: 204 cu. in

Explanation: Split the figure into 2 parts Volume of figure 1: b = 3 in h = 5 in w = 4 in V = 3 in × 4 in × 5 in V = 60 cu. in Volume of figure 2: b = 12 in w = 4 in h = 3 in V = 12 in × 4 in × 3 in V = 144 cu. in Volume of the composite figure = 60 cu in + 144 cu. in = 204 cu. in

Answer: 96 cu ft

Explanation: Split the figure into 3 parts. Figure 1: V1 = 9 ft × 4 ft × 2 ft V1 = 72 cu. ft Figure 2: V2 = 3 ft × 4 ft × 2 ft V2 = 24 cu. ft V = V1 + V2 V = 72 cu. ft + 24 cu. ft = 96 cu. ft Thus the volume of the composite figure is 96 cu. ft

Answer: 300 cu. ft

Answer: 102 cu cm

Question 9. As part of a wood-working project, Jordan made the figure at the right out of wooden building blocks. How much space does the figure he made take up? ______ cu in.

Answer: 784 cu. in

Explanation: Split the figure into 2 parts Figure 1: V1 = 14 in × 4 in × 5 in V1 = 280 cu. in Figure 2: V2 = 12 in × 14 in × 3 in V2 = 504 cu. in V = V1 + V2 V = 280 cu. in + 504 cu. in V = 784 cu. in

Question 10. What are the dimensions of the two rectangular prisms you used to find the volume of the figure? What other rectangular prisms could you have used? Type below: ________

Answer: Dimensions for figure 1: Base = 14 in Width = 4 in Height = 5 in Dimensions for figure 2: Base = 12 in Width = 14 in Height = 3 in

Question 11. If the volume is found using subtraction, what is the volume of the empty space that is subtracted? Explain. ______ cu in.

Answer: 560 cu. in

Explanation: B = 8 in H = 5 in W = 14 in V = 8 in × 14 in × 5 in V = 560 cu. in Thus the volume of the empty space is 560 cu. in

Question 12. Explain how you can find the volume of composite figures that are made by combining rectangular prisms. Type below: ________

Answer: 476 cubic centimeters

Explanation: Split the figure into 2 parts Figure 1: V1 = 10 cm × 7 cm × 5 cm V1 = 350 cu. cm Figure 2: V2 = 3 cm × 7 cm × 6 cm V2 = 126 cu. cm V = V1 + V2 V = 350 cu. cm + 126 cu. cm V = 476 cu. cm

Question 1. Fran drew a triangle with no congruent sides and 1 right angle. Which term accurately describes the triangle? Mark all that apply. Options: a. isosceles b. scalene c. acute d. right

Answer: Right

Explanation: A right triangle is a type of triangle that has one angle that measures 90°. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry. Thus the correct answer is option D.

Answer: Volume of the box is l × w × h V = 8 in × 10 in × 3 in V = 240 cu. in Thus the volume of the box is 240 cu. in

Answer: The figure has 3 sides and 3 angles.

Explanation: From the above figure we can say that there are three sides and three angles.

Answer: a regular polygon If all the sides are congruent then the polygon is a regular polygon.

Answer: 36 cubic feet

Explanation: Figure 1: length = 2 ft width = 3 ft height = 1 ft Volume of 1st figure = l × w × h V = 2 ft × 3 ft × 1 ft = 6 cu. ft Figure 2: length = 4 ft width = 3 ft height = 1 ft Volume of 1st figure = l × w × h V = 4 ft × 3 ft × 1 ft = 12 cu. ft Figure 3: length = 6 ft width = 3 ft height = 1 ft Volume of 1st figure = l × w × h V = 6 ft × 3 ft × 1 ft = 18 cu. ft Add all the volumes = 6 cu. ft + 12 cu. ft + 18 cu. ft Volume = 36 cu. ft

Explanation: Count the number of unit cubes in the first figure. There are 10 unit cubes in figure 1 so match the figure 1 to 10 unit cubes. Count the number of unit cubes in the second figure. There are 12 unit cubes in figure 2 so match figure 2 to 12 unit cubes. Count the number of unit cubes in the third figure. There are 9 unit cubes in figure 3 so match figure 3 to 9 unit cubes.

Question 6. Chuck is making a poster about polyhedrons for his math class. He will draw figures and organize them in different sections of the poster. Part A Chuck wants to draw three-dimensional figures whose lateral faces are rectangles. He says he can draw prisms and pyramids. Do you agree? Explain your answer. i. yes ii. no

Explanation: The lateral faces of a pyramid are triangles. The lateral faces of a prism are rectangles.

Question 6. Part B Chuck says that he can draw a cylinder on his polyhedron poster because it has a pair of bases that are congruent. Is Chuck correct? Explain your reasoning. i. yes ii. no

Explanation: A cylinder does have 2 congruent bases, but a cylinder is not a polyhedron. A cylinder has 1 curved surface, while a polyhedron has faces that are polygons

Answer: 8, 8 The above figure has 8 sides and 8 angles.

Answer: The polygon with 8 sides is known as the octagon. The above figure is congruent thus it is a regular octagon.

Explanation: Given, l = 6 in w = 3 in h = 4 in The volume of the rectangular prism is l × w × h V = 6 in × 3 in × 4in V = 72 cu in. Hence, the volume of the rectangular prism Victoria built is 72 cu. in.

Explanation: The above different have different sizes thus the triangle is scalene. The angle for the above triangle is more than 90° thus the angle is an obtuse angle. So, the answer is yes.

Explanation: The above different have different sizes thus the triangle is scalene. It has one right angle thus the statement is not correct.

Question 10. A shipping crate holds 20 shoeboxes. The dimensions of a shoebox are 6 inches by 4 inches by 12 inches. For 10a–10b, select True or False for each statement. a. Each shoebox has a volume of 22 cubic inches. i. True ii. False

Answer: False

Explanation: Shoebox volume: V = 6 in × 4 in × 12 in V = 288 cu. in Thus the statement is false.

Question 10. b. Each crate has a volume of about 440 cubic inches. i. True ii. False

Explanation: Crate Volume: V = 288 cu. in × 20 V = 5760 cu. in Thus the statement is false.

Question 10. c. If the crate could hold 27 shoeboxes the volume of the crate would be about 7,776 cubic inches. i. True ii. False

Answer: True

Explanation: Crate Volume: V = 288 cu. in × 27 V = 7776 cu. in Thus the statement is true.

Question 11. Part B Mario claims that a rhombus is sometimes a square, but a square is always a rhombus. Is he correct? Explain your answer. i. yes ii. no

Explanation: A square is a quadrilateral with all sides equal in length and all interior angles right angles. A square however is a rhombus since all four of its sides are of the same length.

Explanation: Prism: In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy of the first, and n other faces joining corresponding sides of the two bases. Figure B and C are prisms Pyramid: In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle called a lateral face. All the edges meet at the same point in the pyramid. Thus the figures A and D are pyramids.

Explanation: Mark packed 1-inch cubes into a box with a volume of 120 cubic inches. By seeing the figure we can say that there are 24 unit cubes. To find the number of layers we need to divide 120 by 24 = 120 ÷ 24 = 5 There are 5 layers of 1-inch cubes.

Answer: 312

Explanation: Split the figure into 2 parts. Figure 1: h = 3 cm w = 6 cm b = 4 cm V = 4 cm × 6 cm × 3 cm = 72 cu. cm Figure 2: b = 10 cm w = 6 cm h = 4 cm V = 10 cm × 6 cm × 4 cm = 240 cu. cm Now add the volume of 2 figures 72 cu. cm + 240 cu. cm = 312 cu cm Thus the volume of the composite figure is 312 cu. cm

Answer: rectangle

Explanation: Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

Answer: square

Explanation: A square is a quadrilateral with all sides equal in length and all interior angles right angles.

Answer: trapezoid

Explanation: A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid.

Question 16. Megan’s aquarium has a volume of 4,320 cubic inches. Which could be the dimensions of the aquarium? Mark all that apply. Options: a. 16 in. by 16 in. by 18 in. b. 14 in. by 18 in. by 20 in. c. 12 in. by 15 in. by 24 in. d. 8 in. by 20 in. by 27 in.

Answer: C, D

Explanation: The volume of a prism = l × w × h 1. V = 16 in × 16 in × 16 in V = 4608 cu. in 2. V = 14 in × 18 in × 20 in = 5040 cu. in 3. V = 12 in × 15 in × 24 in = 4320 cu. in 4. V = 8 in × 20 in × 27 in = 4320 cu in Thus the suitable answers are C and D.

Question 17. Ken keeps paper clips in a box that is the shape of a cube. Each side of the cube is 3 inches. What is the volume of the box? ______ cubic inches

Explanation: Ken keeps paper clips in a box that is the shape of a cube. Each side of the cube is 3 inches. The volume of a cube = 3 in × 3 in × 3 in = 27 cu. in Therefore the volume of the box is 27 cubic inches.

Explanation: Monica used 1-inch cubes to make the rectangular prism Volume = 1 in × 1 in × 1 in = 1 cu. in. Each cube has a volume of 1 cubic inch.

Question 18. b. Each layer of the prism is made up of ____ cubes. ______ cubes

Explanation: We can calculate the layer by calculating the base and width 4 × 5 = 20 cubes Each layer of the prism is made up of 20 cubes.

Question 18. c. There are ____ layers of cubes. ______ layers

Answer: 3 By seeing the figure we can say that there are 3 layers of the cube. You can also find the layers of the cube by calculating the height of the figure.

Question 18. d. The volume of the prism is ____ cubic inches. ______ cubic inches

Explanation: The volume of a prism = l × w × h V = 4 in × 5 in × 3 in Volume = 60 cu. inches Therefore, the volume of the prism is 60 cubic inches.

Chapter Review/Test – Vocabulary – Page No. 4910

Question 1. A _____ has two congruent polygons as bases and rectangular lateral faces. __________

Answer: prism A prism has two congruent polygons as bases and rectangular lateral faces.

Question 2. A _____ has only one base and triangular lateral faces. __________

Answer: pyramid A pyramid has only one base and triangular lateral faces.

Answer: i. hexagon ii. regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure has six sides and 6 angles. Thus the name of the polygon is hexagon. Two polygons are congruent when they have the same size and the same shape. The above figure has same size and angles. Thus it is a regular polygon.

Answer: i. pentagon ii. regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure has five sides and 5 angles. Thus the name of the polygon is pentagon. Two polygons are congruent when they have the same size and the same shape. The above figure has same size and angles. Thus it is a regular polygon.

Answer: i. pentagon ii. not regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure has five sides and 5 angles. Thus the name of the polygon is the pentagon. Two polygons are congruent when they have the same size and the same shape. The above figure does not have the same size and angles. Thus it is not a regular polygon.

Answer: i. octagon ii. not regular

Explanation: A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. The above figure has 8 sides and 8 angles. Thus the name of the polygon is octagon. Two polygons are congruent when they have the same size and the same shape. The above figure does not have same size and angles. Thus it is not a regular polygon.

Classify each figure in as many ways as possible.

Answer: 1. quadrilateral 2. trapezoid

Explanation: 1. A general quadrilateral has 4 sides and 4 angles. 2. A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel.

Answer: △ – scalene ∠ – right

Explanation: The above triangle has different sides. Thus the triangle is a scalene triangle. The triangle with one right angle is known as a right angled triangle.

Answer: prism

Explanation: In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

Answer: pyramid

Explanation: In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the vertex). Like any pyramid, it is self-dual.

Explanation: The figure shows that there are 4 unit cubes.

Explanation: By seeing the above figure we can say that there are 7 unit cubes.

Explanation: The figure above shows that there are 5 unit cubes.

Answer: obtuse; scalene

Explanation: The sides of the triangle is different. Thus it is a scalene triangle. The angle of the triangle is an obtuse angle. Thus the correct answer is option C.

Answer: 7 faces, 12 edges, 7 vertices

Explanation: In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point. The hexagonal pyramid has 7 faces, 12 edges and 7 vertices. Therefore the correct answer is option C.

Question 16. A manufacturing company constructs a shipping box to hold its cereal boxes. Each cereal box has a volume of 40 cubic inches. If the shipping box holds 8 layers with 4 cereal boxes in each layer, what is the volume of the shipping box? Options: a. 160 cu in. b. 320 cu in. c. 480 cu in. d. 1,280 cu in.

Answer: 1,280 cu in.

Explanation: A manufacturing company constructs a shipping box to hold its cereal boxes. Each cereal box has a volume of 40 cubic inches. If the shipping box holds 8 layers with 4 cereal boxes in each layer Multiply the number of layers with boxes = 8 × 4 = 32 The volume of 8 layers is 40 × 32 = 1280 cubic inches Thus the correct answer is option D.

Question 17. Sharri packed away her old summer clothes in a storage tote that had a length of 3 feet, a width of 4 feet, and a height of 3 feet. What was the volume of the tote that Sharri used? Options: a. 36 cu ft b. 24 cu ft c. 21 cu ft d. 10 cu ft

Answer: 36 cu ft

Explanation: Given, Sharri packed away her old summer clothes in a storage tote that had a length of 3 feet, a width of 4 feet, and a height of 3 feet. Volume = l × w × h V = 3 ft × 4 ft × 3 ft V = 36 cu. ft Thus the volume of the tote that Sharri used is 36 cu. ft. The correct answer is option A.

Explanation: The opposite sides of figure b are not parallel. Thus the figure b quadrilateral is NOT classified as a parallelogram.

Answer: Volume of 1st cube is 5 cm × 4 cm × 5 cm = 100 cu. cm Volume of 2nd cube is 5 cm × 4 cm × 8 cm = 160 cu. cm Volume of 3rd cube is 5 cm × 4 cm × 5 cm = 100 cu. cm Add all the volumes to find the volume of the composite figure That means 100 cu. cm + 160 cu. cm + 100 cu. cm = 360 cu. cm Therefore the volume of the composite figure is 360 cm 3 The correct answer is option C.

Constructed Response

Answer: 512 cu. ft

Explanation: length = 2 ft width = 2 ft height = 2 ft Volume of the display of game console boxes = 2 ft × 2 ft × 2 ft = 8 cu. ft Number of console boxes = 64 64 × 8 cu. ft = 512 cu ft The volume of the display of game console boxes = 512 cu ft

Question 20. b. On a busy Saturday, the video game store sold 22 game consoles. What is the volume of the game console boxes that are left? _____ cu ft.

Answer: 336 cu. ft

length = 2 ft width = 2 ft height = 2 ft The volume of the display of game console boxes = 2 ft × 2 ft × 2 ft = 8 cu. ft Number of console boxes = 22 The volume of the game console boxes that are left 22 × 8 cu. ft = 176 cu. ft The volume of the game console boxes that are left = 512 – 176 = 336 cu. ft

Performance Task

Question 21. Look for two pictures of three-dimensional buildings in newspapers and magazines. The buildings should be rectangular prisms. A. Paste the pictures on a large sheet of paper. Leave room to write information near the picture. B. Label each building with their name and location. C. Research the buildings, if the information is available. Find things that are interesting about the buildings or their location. Also find their length, width, and height to the nearest foot. If the information is not available, measure the buildings on the page in inches or centimeters, and make a good estimate of their width (such as 1/2 the height, rounded to the nearest whole number). Find their volumes. D. Make a class presentation, choosing one of the buildings you found.

Conclusion:

Follow our Go Math Grade 5 Answer Key Chapter 11 Geometry and Volume to get the step by step explanation. So, Download the pdf of HMH Go Math 5th Grade Solution Key Chapter 11 Geometry and Volume for free. Click on the above links and find the question and answers with images. Do not move to anywhere, stay on Go Math, and follow them each and every question of Geometry and Volume with explanation and strengthen your math skills.

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enVision Math Common Core Grade 5 Answer Key Topic 11 Understand Volume Concepts

Go through the  enVision Math Common Core Grade 5 Answer Key  Topic 11 Understand Volume Concepts  regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 11 Understand Volume Concepts

enVision STEM Project: Everyday Energy Do Research Use the Internet and other sources to learn more about these five types of energy: electrical, light, mechanical, sound, and thermal. Make a table of the various types of energy you use every day. Include at least one example of how you use each type of energy.

Journal: Write a Report Include what you found. Also in your report: • Draw a diagram of your classroom and label where and how 3 types of energy are used. • Estimate how far your desk is from a light energy source and add this dimension to your sketch. • Use your diagram to make up and solve problems involving measurements such as the volume of your classroom.

Review What You Know

A-Z Vocabulary

Choose the best term from the box. Write it on the blank.

• compensation • partial products • rectangle • unit fraction

Question 1. Adjusting a number to make a computation easier and balancing the adjustment by changing another number is called ____ Answer:

Adjusting a number to make a computation easier and balancing the adjustment by changing another number is called compensation

Question 2. A fraction with a numerator of 1 is called a ____ Answer:

A fraction with a numerator of 1 is called a  unit fraction

Question 3. A quadrilateral with 2 pairs of parallel sides that are the same length and 4 right angles is a ____ Answer:

A quadrilateral with 2 pairs of parallel sides that are the same length and 4 right angles is a rectangle

Area Find the area of each figure.

From the figure,

Length = 10h

breadth =6h

Area of rectangle = Length x Breadth = 10h x 6h = 60h^2

Length = 12cm

breadth = 8cm

Area of rectangle = Length x Breadth = 12cm x 8cm = 96cm^2

Find each product or quotient.

Question 6. 16 × 6 Answer:

Question 7. 3 × 42 Answer:

Question 8. 216 ÷ 3 Answer:

Question 9. 128 ÷ 4 Answer:

Question 10. (5 × 6) × 3 Answer:

(5 × 6) × 3

Question 11. (6 × 6) × 6 Answer:

(6 × 6) × 6

Question 12. Joanie has two 12-inch-long wood pieces and two 16-inch-long wood pieces. What is the combined length of the wood pieces? A. 28 inches B. 32 inches C. 56 inches D. 192 inches Answer:

Number of 12 inch wood pieces = 2 = 12 x 2 = 24

Number of 16 inch wood pieces = 2 = 16 x 2 = 32

combined length of the wood pieces = 24 + 32 = 56

C. 56 inches is correct

Finding Area

Question 13. Niko used square tiles to make a rectangle with 2 rows and 7 tiles in each row. Explain how you can find the area of the rectangle. Answer:

Pick a Project

3-ACT MATH PREVIEW

Math Modeling

Fill ‘er Up

Lesson 11.1 Model Volume

Solve & Share Gina is building a rectangular prism out of sugar cubes for her art class project. She started by drawing a diagram of the rectangular prism that is 4 cubes high, 4 cubes long and 2 cubes wide. How many cubes does she use to make the prism? Solve this problem any way you choose.

Use Appropriate Tools You can use cubes to build a rectangular prism and then draw a picture to show the different faces. Show your work!

Visual Learning Bridge

Essential Question How Can You Measure Space Inside a Solid Figure?

Guided Practice

Do You Understand?

Question 1. Make a model of a rectangular prism with a bottom layer that is 3 cubes long by 3 cubes wide. Make a top layer that is the same as the bottom layer. Then draw a picture of your model. What is the volume? Answer:

Each cube of a solid figure is 1 cubic unit.

There are 9 unit cubes in the bottom layer. The volume of the bottom layer is 9 cubic units.

Multiply the volume of the bottom layer by 2.

The volume of the prism is 2 × 9 or 18 cubic units.

Question 2. A-Z Vocabulary What is the difference between a unit cube and a cubic unit? Answer:

A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.

Do You Know How?

In 3 and 4, use unit cubes to make a model of each rectangular prism. Find the volume.

There are 4 unit cubes in the bottom layer. The volume of the bottom layer is 4 cubic units.

The volume of the prism is 2 × 4 or 8 cubic units.

There are 12 unit cubes in the bottom layer. The volume of the bottom layer is 12 cubic units.

The volume of the prism is 12 × 1 or 12 cubic units.

Independent Practice

In 5-13, find the volume of each solid. Use unit cubes to help.

Multiply the volume of the bottom layer by 3.

The volume of the prism is 9 × 3 or 27 cubic units.

There are 8 unit cubes in the bottom layer. The volume of the bottom layer is 8 cubic units.

The volume of the prism is 8 × 3 or 24 cubic units.

There are 20 unit cubes in the bottom layer. The volume of the bottom layer is 20 cubic units.

The volume of the prism is 20 × 2 or 40 cubic units.

The volume of the prism is 8 × 2 or 16 cubic units.

There are 2 unit cubes in the bottom layer. The volume of the bottom layer is 2 cubic units.

Multiply the volume of the bottom layer by 5.

The volume of the prism is 2 × 5 or 10 cubic units.

There are 6 unit cubes in the bottom layer. The volume of the bottom layer is 6 cubic units.

The volume of the prism is 6 × 3 or 18 cubic units.

The volume of the prism is 12 × 3 or 36 cubic units.

The volume of the prism is 12 × 2 or 24 cubic units.

There are 10 unit cubes in the bottom layer. The volume of the bottom layer is 10 cubic units.

The remaining cubes are 4 x 3 or 12 and the volume is 12 cubic units

The volume of the prism is 10 + 12 or 22 cubic units.

Problem Solving

In 14-18, use the table.

Prism A > Prism B

Prism B = Prism C

Prism C < Prism A

Question 17. If you added another layer of unit cubes on top of Prism A, what would the volume of the new solid be in cubic units? Answer:

Question 18. If you put Prism C on top of Prism A, what would the volume of the new solid be in cubic units? Answer:

The volume of A is 16 cubic units

The volume of C is 6 cubic units

If you put Prism C on top of Prism A, Then the volume is 16 + 6 or 22 cubic units

Question 19. Reasoning In an election, 471 people voted. Candidate B received \(\frac{2}{3}\) of the votes. How many votes did Candidate B receive? Answer:

Number of votes voted = 471

Candidate B received 2/3 of the votes

Number of votes B received = 2/3 x 471 =314

Question 20. Higher Order Thinking Ms. Kellson’s storage closet is 3 feet long, 3 feet wide, and 7 feet high. Can she fit 67 boxes that each have a volume of 1 cubic foot in her closet? Explain your answer. Answer:

Multiply the volume of the bottom layer by 7.

The volume of the prism is 9 × 7 or 63 cubic units.

She can not fit 67 boxes that each have a volume of 1 cubic foot in her closet.

Assessment Practice

C. The volume of Model X is 19 cubic units greater than the volume of Model Y.

Essential Question How Can You Use a Formula to Find Stor the Volume of a Rectangular Prism?

Convince Me! Reasoning Give the dimensions of a different rectangular prism that also has a volume of 72 ft 3 . Explain how you decided.

Question 1. In the Example on page 462, could you first multiply the width by the height? Explain. Answer:

Question 2. A wooden block measures 5 centimeters tall, 3 centimeters wide, and 2 centimeters long. The area of the base is 6 centimeters. Draw a rectangular prism to show the block and label it. What is the volume of the block? Answer:

In 3 and 4, find the volume of each rectangular prism.

Volume = length × width × height V = l × w × h V = (9 × 2) × 4 V = 18 × 4 V = 72 The volume of the rectangular prism is 72 cubic inch or 72 in 3 .

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 24 × 9 V = 216 yd 3

In 5-10, find the volume of each rectangular prism.

Volume = length × width × height V = l × w × h V = (7 × 4) × 3 V = 28 × 3 V = 84

The volume of the rectangular prism is 84 cubic cm or 72 cm 3 .

Volume = length × width × height V = l × w × h V = (4 × 4) × 5 V = 16 × 5 V = 80 The volume of the rectangular prism is 80 cubic inch or 80 in 3 .

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 52 × 3 V = 156 m 3

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 64 × 4 V = 256 cm 3

Volume = length × width × height V = l × w × h V = (7 × 7) × 7 V = 49 × 7 V = 343 The volume of the rectangular prism is 343 cubic meter or 343 m 3 .

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 153 × 7 V = 1071 cm 3

Volume = length × width × height V = l × w × h V = (7 × 3) × 9 V = 21 × 9 V = 189 The volume of the rectangular prism is 189 cubic inch or 189 in 3 .

Question 7.

The volume of a First oven is V = b × h, where b is the area of the base. V = b × h. V = 576 × 15 V = 8640 in 3

The volume of a second oven is V = b × h, where b is the area of the base. V = b × h. V = 672 × 14 V = 9408 in 3

The second oven has greater volume and 768 in 3 greater than the first one.

Question 13. The perimeter of an equilateral triangle is 51 feet. What is the length of one of its sides? Explain your work. Answer:

The formula of the perimeter of an equilateral triangle is 3a, where a is the length of one side.

Given, The perimeter of an equilateral triangle is 51 feet

a = 51/3 = 17

Therefore, the length of one of its sides is 17 and all sides are equal.

Question 14. Reasoning Harry is in line at the store. He has three items that cost $5.95, $4.25, and $1.05. Explain how Harry can add the cost of the items mentally before he pays for them. Answer:

Harry has three items that cost $5.95, $4.25, and $1.05.

$5.95 approximately equals $6

$4.25  approximately equals $4

$1.05 approximately equals $1

Therefore, by approximation, Harry can add the cost of the items mentally before he pays for them.

$6 + $4 + $1 = $11. (approximately)

Lesson 11.3 Combine Volumes of Prisms

Solve & Share Ariel is thinking of a three-dimensional figure that is made by combining two rectangular prisms. What is the volume of this three-dimensional figure? Solve this problem any way you choose.

Look Back! How did you separate the solid into simpler rectangular prisms? Write the dimensions of each of the prisms.

Essential Question How Can You Find the Volume of a Solid Figure question Composed of Two Rectangular Prisms?

Convince Me! Reasoning What is another way to divide the solid above into two rectangular prisms? What are the dimensions of each prism?

In 1 and 2, use the solid below. The dashed line separates it into two rectangular prisms, A and B.

Question 1. What are the length, width, and height of Prism A? What are the length, width, and height of Prism B? Answer:

length, width, and height of Prism A are 4 ft, 3 ft, 12 ft respectively.

length, width, and height of Prism B are 3 ft, 2 ft, 5 ft respectively.

Question 2. What is another way you could separate the shape into two rectangular prisms? What are each prism’s dimensions? Answer:

Bisecting the figure horizontally, another way I could separate the shape into two rectangular prisms.

length, width, and height of Prism A are 4 ft, 3 ft, 7 ft respectively.

length, width, and height of Prism B are 6 ft, 3 ft, 5 ft respectively.

In 3 and 4, find the volume of each solid figure.

Volume = length × width × height Volume of A = l × w × h V = (5 × 7) × 8 V = 35 × 8 V = 280

The volume of the A is 280 cubic in or 280 in 3 .

Volume = length × width × height Volume of B  = l × w × h V = (10 × 7) × 2 V = 70 × 2 V = 140

The volume of the B is 140 cubic in or 140 in 3 .

Combined Volume  of Solid Figure is 280 in 3 + 140 in 3  = 420 in 3 

Volume = length × width × height Volume of A = l × w × h V = (5 × 8) × 5 V = 40 × 5 V = 200

The volume of the A is 200 cubic cm or 200 cm 3 .

Volume = length × width × height Volume of B  = l × w × h V = (7 × 8) × 2 V = 56 × 2 V = 112

The volume of the B is 112 cubic cm or 112 cm 3 .

Combined Volume  of Solid Figure is 200 cm 3 + 112 cm 3  = 312 in 3

In 5-7, find the volume of each solid figure.

Volume = length × width × height Volume of A = l × w × h V = (8 × 4) × 7 V = 32 × 7 V = 224

The volume of the A is 224 cubic cm or 224 cm 3 .

Volume = length × width × height Volume of B  = l × w × h V = (6 × 4) × 3 V = 24 × 3 V = 72

The volume of the B is 72 cubic cm or 72 cm 3 .

Combined Volume  of Solid Figure is 224 cm 3 + 72 cm 3  = 296 cm 3

Volume = length × width × height Volume of A = l × w × h V = (6 × 10) × 5 V = 60 × 5 V = 300

The volume of the A is 300 cubic ft or 300 ft 3 .

Volume = length × width × height Volume of B = l × w × h V = (6 × 2) × 4 V = 12 × 4 V = 48

The volume of the B is 48 cubic ft or 48 ft 3 .

Combined Volume  of Solid Figure is 300 ft 3 + 48 ft 3  = 348 ft 3

Volume = length × width × height Volume of A = l × w × h V = (4 × 6) × 12 V = 24 × 12 V = 288

The volume of the A is 288 cubic m or 288 m 3 .

Volume = length × width × height Volume of B  = l × w × h V = (9 × 5) × 12 V = 45 × 12 V = 540

The volume of the B is 540 cubic m or 540 m 3 .

Combined Volume  of Solid Figure is 288 m 3 + 540 m 3  = 828 m 3

For 8-10, use the drawing of the solid figure.

Question 8. How would you find the volume of the figure shown? Answer:

Question 9. Algebra Write two Expressions that can be added to find the volume of the solid figure. Answer:

Volume = length × width × height Volume of A = l × w × h V = (5 × 4) × 10 V = 20 × 10 V = 200

The volume of the A is 200 cubic m or 200 m 3 .

Volume = length × width × height Volume of B  = l × w × h V = (5 × 2) × 7 V = 10 × 7 V = 70

The volume of the B is 70 cubic m or 70 m 3 .

Question 10. What is the volume of the solid figure? Answer:

Combined Volume  of Solid Figure is 200 m 3 + 70 m 3  = 270 m 3

Question 11. Higher Order Thinking A solid figure is separated into two rectangular prisms. The volume of Rectangular Prism A is 80 cubic feet. Rectangular Prism B has a length of 6 feet and a width of 5 feet. The total volume of the solid figure is 200 cubic feet. What is the height of Rectangular Prism B? Show your work. Answer:

Volume of A  = length × width × height V = l × w × h V = (6 × 10) × 5 V = 60 × 5 V = 300

The volume of the rectangular prism is 300 cubic in or 300 in 3 .

Volume of B  = length × width × height V = l × w × h V = (10 × 10) × 2 V = 100 × 2 V = 200

The volume of the rectangular prism is 200 cubic in or 200 in 3 .

Total volume =  200 in 3 + 300 in 3  = 500 in 3

Lesson 11.4 Solve Word Problems Using Volume

Solve & Share A school has two wings, each of which is a rectangular prism. The school district is planning to install air conditioning in the school and needs to know its volume. What is the volume of the school? Solve this problem any way you choose.

Look Back! Write a mathematical Expression that can be used to find the total volume of the school.

Essential Question How Can You Use Volume Formulas to Solve Real-World Problems?

You can make sense of the problem by breaking it apart into simpler problems.

B. Find the volume of each section. Use the formula V = l × w × h. Small section: V = 4 × 3 × 8 = 96 Large section: V = 10 × 6 × 8 = 480 Add to find the total volume: 96 + 480 = 576 The combined volume is 576 cubic feet.

Convince Me! Critique Reasoning Tom solved the problem in a different way. First, he found the total area of the floor, and then he multiplied by the height. Does Tom’s method work? Explain.

Question 2. What is the height of the top section of the china cabinet? Explain.

Height of the top section of the china cabinet is 4 ft

Because, 7 ft – 3 ft = 4 ft

Question 3. Find the volume of the china cabinet. Answer:

Volume of china cabinet  = length × width × height V = l × w × h V = (4 × 1) × 4 V = 4 × 4 V = 16

The volume of the rectangular prism is 16 cubic ft or 16 ft 3 .

Volume of A = length × width × height V = l × w × h V = (35 × 54) × 82 V = 1890 × 82 V = 154,980

The volume of the rectangular prism is 154,980 cubic ft or 154,980 ft 3 .

Volume of B = length × width × height V = l × w × h V = (40 × 30) × 50 V = 1200 × 50 V = 60000

The volume of the rectangular prism is 60000 cubic ft or 60000 ft 3

Therefore, Combined volume is  154,980 ft 3 + 60000 ft 3  = 214,980 ft 3

Question 5. The nature center has a fish tank shaped like a rectangular prism that measures 6 feet long by 4 feet wide by 4 feet high. It can be stocked safely with 3 small fish in each cubic foot of water. How many small fish can safely fit in the tank? Answer:

Volume of rectangular prism  = length × width × height V = l × w × h V = (6 × 4) × 4 V = 24 × 4 V = 96

The volume of the rectangular prism is 96 cubic ft or 96 ft 3 .

If it can be stocked safely with 3 small fish in each cubic foot of water. Then 96/3 = 12

12 fish can be stocked safely with 3 small fish in each cubic foot of water.

Volume of A = length × width × height V = l × w × h V = (3 × 5) × 10 V = 15 × 10 V = 150

The volume of the rectangular prism is 150 cubic cm or 150 cm 3 .

Volume of B = length × width × height V = l × w × h V = (20 × 24) × 20 V = 480 × 20 V = 9600

The volume of the rectangular prism is 9600 cubic cm or 9600 cm 3

Therefore, Combined volume is  150 cm 3 + 9600 cm 3  = 9750 cm 3

Volume of first stair = length × width × height V = l × w × h V = (40 × 10) × 7 V = 400 × 7 V = 2800

The volume of the first stair is 2800 cubic in or 2800 in 3 .

Volume of Second stair = length × width × height V = l × w × h V = (40 × 10) × 14 V = 400 × 14 V = 5600

The volume of the second stair is 5600 cubic in or 5600 in 3

Volume of third stair = length × width × height V = l × w × h V = (40 × 10) × 21 V = 400 × 21 V = 8400

The volume of the rectangular prism is 8400 cubic in or 8400 in 3

Therefore, Combined volume is  2800 in 3 + 5600 in 3 + 8400 in 3  = 16800 in 3

16800 cubic inches of concrete it takes to make these stairs

Volume of bedroom = length × width × height V = l × w × h V = (14 × 12) × 9 V = 168 × 9 V = 1512

The volume of the second stair is 1512 cubic ft or 1512 ft 3

Volume of  closet = length × width × height V = l × w × h V = (3 × 4) × 7 V = 12 × 7 V = 84

The volume of the rectangular prism is 84 cubic ft or 84 ft 3

Therefore, Combined volume is  1512 ft 3 + 84 ft 3    = 11596 ft 3

Question 9. Critique Reasoning Does it make sense for Angelica to find the combined area of the bedroom floor and closet floor before finding the total volume? Explain your thinking. Answer:

Yes. the total volume is sum of the bedroom and closet of Angelica room

Volume of building = length × width × height V = l × w × h V = (64 × 60) × 28 V = 3840 × 28 V = 107,520

The volume of the second stair is 107,520 cubic m or 107,520 m 3

Volume of open air courtyard = length × width × height V = l × w × h V = (18 × 30) × 28 V = 540 × 28 V = 15120

The volume of the rectangular prism is 15120 cubic m or 15120 m 3

Therefore, Total volume of building is  107,520 m 3 – 15120 m 3   = 92400 m 3

Volume of first section = length × width × height V = l × w × h V = (5 × 4) × 8 V = 20 × 8 V = 160

The volume of the first section is 160 cubic ft or 160 ft 3

Volume of open second section = length × width × height V = l × w × h V = (3 × 2) × 8 V = 6 × 8 V = 48

The volume of the second section is 48 cubic ft or 48 ft 3

Therefore, the total volume of the building is  160 ft 3 + 48 ft 3   = 208 ft 3

If she needs one box for every 32 cubic feet of space. Then Number of boxes = 208 / 32 = 6.5

She needs 6 or 7 boxes.

Lesson 11.5 Use Appropriate Tools

Solve & Share A space station is being built from 24 cubic modules. The space station can be any shape but the modules must be placed together so that entire faces match up with each other. Choose a tool to create two different plans for the space station. Explain why you chose the tool you selected.

Look Back! Use Appropriate Tools How did you decide which tool to use?

Essential Question How Can You Use Appropriate Tools question to Solve Volume Problems?

What do I need to do? I need to choose an appropriate tool to solve this problem.

B. How can I use appropriate tools strategically to help me solve this problem? I can • decide which tool is appropriate. • use cubes to solve this problem. • use the tool correctly.

Convince Me! Use Appropriate Tools What tools other than cubes could you use to solve this problem? Explain.

Use Appropriate Tools A paint store manager is going to build a display with same-sized cubes. The display will look like a staircase with 5 steps. Each step in the display will be 6 cubes long. The store manager will build the staircase display with 1-foot plastic cubes.

Question 1. What tool might the manager use to be sure that there is enough space for the display? Explain. Answer:

Question 2. What is the volume of the display? Explain how you used tools to decide. Answer:

Use Appropriate Tools

Cindy plans to make a jewelry box shaped like a rectangular prism. She wants it to have a volume of 96 cubic inches.

Question 3. How can you find possible dimensions of the box? Answer:

Question 4. What could the dimensions of that jewelry box be? Answer:

Question 5. Can Cindy build the box so that it is twice as wide as it is tall? Answer:

Question 6. Cindy has some ribbon to decorate the jewelry box. What tool might help her decide how much of the jewelry box she can decorate? Answer:

Problem Solving Performance Task

Remember to think about which tools make sense for these problems.

Question 7. Use Structure What is the total volume of a planter that has a 6 × 6 opening? Answer:

Question 8. Use Structure What is the total volume of a planter that has an 8 × 8 opening? Answer:

Question 9. Use Appropriate Tools What will be the total volume of a planter that has a 12 × 12 opening? Can you determine this by just using paper and pencil? Explain. Answer:

Question 10. Model with Math Each concrete cube used to make the planters costs $3.00. What is the total cost of the cubes needed for two planters with 6 × 6 openings, two with 8 × 8 openings, and two with 12 × 12 openings? Write an Expression that represents the total cost. Answer:

Topic 11 Fluency Practice

Find a Match

Work with a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box above the match. Find a match for every clue.

Topic 11 Vocabulary Review

Understand Vocabulary

In 1-3, choose the best term from the Word List. Write it on the blank. • area • cubic unit • formula • rectangular prism • unit cube • volume

Question 1. The number of same-size unit cubes that fill a solid figure without overlaps or gaps in the figure’s ____ Answer:

The number of same-size unit cubes that fill a solid figure without overlaps or gaps in the figure’s volume

Question 2. A solid figure with 6 rectangular faces that are not all squares is a(n) ___ Answer:

A solid figure with 6 rectangular faces that are not all squares is a rectangular prism

Question 3. A rule that uses symbols to relate two or more quantities is a(n) ___. Answer:

A rule that uses symbols to relate two or more quantities is a formula

Draw a line from each three-dimensional figure in Column A to its volume in Column B.

Question 8. One box is 3 inches by 4 inches by 5 inches. A second box is 4 inches by 4 inches by 4 inches. Explain how to decide which box holds more. Answer:

Volume of the first box is, V = 3 x 4 x 5 = 60 cubic inches.

Volume of the second box is, V = 4 x 4 x 4 = 64 cubic inches.

The second box holds more because it has more volume.

Topic 11 Reteaching

Set A pages 457-460

Remember that you can find the number of cubes in each layer and then multiply by the number of layers.

Find each volume. You may use cubes to help.

There are 14 unit cubes in the bottom layer. The volume of the bottom layer is 14 cubic units.

The volume of the prism is 14 × 2 or 28 cubic units.

The volume of the prism is 10 × 2 or 20 cubic units.

The volume of the prism is 12 × 6 or 72 cubic units.

Remember if you know the area of the base of a rectangular prism, use the formula V = b × h, where b is the area of the base.

Question 1. Area of the base, b = 42 square meters and height = 3 meters Answer:

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 42 × 3 V = 126 m 3

Question 2. Area of the base = 75 square inches and height = 15 inches Answer:

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 75 × 15 V = 1125 in 3

Volume = length × width × height Volume = l × w × h V = (8 × 4) × 3 V = 32 × 3 V = 96

The volume of the B is 96 cubic ft or 70 ft 3 .

Set C pages 465-468, 469-472

Remember to identify the length, width, and height of each prism, so that you can calculate the volume of each part.

Volume = length × width × height Volume of A = l × w × h V = (10 × 6) × 2 V = 60 × 2 V = 120

The volume of the A is 120 cubic cm or 120 cm 3 .

Volume = length × width × height Volume of B  = l × w × h V = (2 × 6) × 3 V = 12 × 3 V = 36

The volume of the B is 36 cubic cm or 36 cm 3 .

Combined Volume  of Solid Figure is 120 cm 3 + 36 cm 3  = 156 cm 3

Volume = length × width × height Volume of A = l × w × h V = (70 × 50) × 90 V = 3500 × 90 V = 315,000

The volume of the A is 315,000 cubic m or 315,000 m 3 .

Volume = length × width × height Volume of B  = l × w × h V = (60 × 50) × 20 V = 3000 × 20 V = 60000

The volume of the B is 60000 cubic m or 60000 m 3 .

Combined Volume  of Solid Figure is 315,000 m 3 + 60000 m 3  = 375,000 m 3

Set D pages 473-476 Think about these questions to help you use appropriate tools strategically.

Remember that tools such as place-value blocks, cubes, and grid paper can help you solve problems involving volume.

Question 1. What tools could you use to model the problem? Answer:

Question 2. What is the total volume of the structure? Answer:

Total blocks in bottom layer = 5 x 3 =15

Height =2 ; total volume is 15 x 2 = 30.

blocks left = 3 x 1 x 2 = 6

Therefore, total volume = 30 – 6 = 24 cubic units

Topic 11 Assessment Practice

B. 72 cubic units

Question 3. A. A swimming pool is 50 meters long, 15 meters wide, and 3 meters deep. What is the volume of the pool? A. 4,500 cubic meters B. 2,250 cubic meters C. 900 cubic meters D. 750 cubic meters B. After filling the pool for several minutes, the water is 1 meter deep. What is the volume of water in the pool? Answer:

Volume = length × width × depth Volume of Swimming pool = l × w × h V = (50 × 15) × 3 V = 750 × 3 V = 2250

The volume of the Swimming pool is 2250 cubic m or 2250 m 3 .

Volume = length × width × depth Volume of Swimming pool after filling the pool for several minutes, the water is 1 meter deep = V = (50 × 15) × 4 V = 750 × 4 V = 3000

The volume of the Swimming pool is 3000 cubic m or 3000 m 3 .

Volume = length × width × height Volume of A = l × w × h V = (8 × 12) × 24 V = 96 × 24 V = 2304

The volume of the A is 2304 cubic ft or 2304 ft 3 .

Volume = length × width × height Volume of B  = l × w × h V = (32 × 12) × 16 V = 384 × 16 V = 6114

The volume of the B is 6114 cubic ft or 6114 ft 3

Combined Volume  of Solid Figure is 2304 ft 3 + 6114 ft 3  = 8418 ft 3

Volume = length × width × height Volume of bale of hay  = l × w × h V = (100 × 40) × 30 V = 4000 × 30 V = 120000

The volume of the bale of hay is 120000 cubic cm or 120000 cm 3

Volume = length × width × height Volume of A = l × w × h V = (10 × 9) × 6 V = 90 × 6 V = 540

The volume of the A is 540 cubic in or 540 in 3 .

Volume = length × width × height Volume of B  = l × w × h V = (10 × 5) × 6 V = 50 × 6 V = 300

The volume of the B is 300 cubic in or 300 in 3

Combined Volume  of Solid Figure is 540 in 3 + 300 in 3  = 840 in 3

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. V = 750 × 25 V = 18750 in 3

Option A. V = b × h

Question 8. For her science project, Jada wants to build a rectangular prism out of foam blocks. The prism should have a volume of 350 cubic inches and a height of 5 inches. What does the area of the base of the prism need to be for the given volume and height? Give one pair of possible whole-number dimensions for the base. Answer:

The volume of a rectangular prism is V = b × h, where b is the area of the base. V = b × h. 350 = b × 5 b = 350/5 = 70

The area of the base of the prism needs to be for the given volume and height is 70 in 2

Question 9. Martin’s suitcase has a volume of 1,080 cubic inches. Lily’s suitcase measures 9 inches wide, 13 inches long, and 21 inches high. What is the combined volume of the two suitcases? Answer:

The volume of the first suitcase is 1080 cubic in or 1080 in 3 .

Volume = length × width × height Volume of Second suitcase is  = l × w × h V = (9 × 13) × 21 V = 117 × 21 V = 2457

The volume of the second suitcase is 2457 cubic in or 2457 in 3

The combined volume of both suitcases is 1080 in 3 + 2457 in 3  = 3537 in 3

Topic 11 Performance Task

There are 84 boxes in the Golf Ball Display Part B Explain how the number of boxes you found in Part A is the same as what you would find by using the formula V= l × w ×h.

Each block has volume of 1 cubic unit.

Length = 7 boxes

Breadth = 4 boxes

Height = 3 boxes

Volume is length x breadth x height

V= l × w ×h = 7 x 4 x 3

v = 28 x 3 = 84 cubic units.

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Volume Word Problems Worksheets

How to Find the Volume of Basic Shapes - In geometry, we need to figure out the volume, surface area, and perimeter of the shapes. There are a number of shapes in geometry; each shape has a specific formula for perimeter, surface area, and volume. We should follow those formulae to find out the specific measurement of the shape. Here we are going to discuss the formulae of finding the volume of some of the geometric shapes. Volume of the Sphere - A sphere is a three-dimensional shape. To find out the surface area or volume of the sphere, we need to know the radius of the sphere. The radius of the sphere is the distance from the center to the edge of the sphere. The radius remains the same no matter from which point on a sphere is considered. Once we know the radius, we use the following formula to find out the volume of the sphere. Volume = 4/3 πr 2 . Volume of the Cone - A cone is defined as the pyramid that features a circular base with sloping sides, all meeting at the central point. For calculating the volume of the cone, we need to know the radius of length and base of the side. Volume = 1/3 π 2 h. Volume of the Cylinder - A cylinder is a shape that features a circular base and parallel sides. For calculating the volume of the cylinder, we need to know the height and radius of the cylinder. Volume = πr 2 h.

Basic Lesson

Demonstrates how to outline Volume Word Problems. Example: Find the volume of cube with 7 cm sides. Volume of cube = (side) 3

Intermediate Lesson

Uses slightly larger sentences and numbers than the basic lesson. Example: Find the volume of sphere of radius of 21 inches. Volume of sphere = 4/3 × π × r 3

Independent Practice 1

Contains a series of 20 volume Word Problems. The answers can be found below. Example: A large cylindrical can is to be designed from a rectangular piece of aluminum that is 25 inches long and 10 inches high by rolling the metal horizontally. Determine the volume of the cylinder.

Independent Practice 2

Features 20 word problems. Example: The dimensions of a chamber are 11 ft by 9 ft by 9 ft. The chamber is thought to have been used for storing ammunition had dimensions of 1 ft by 1 ft by 3 ft. What is the maximum number of ammunition boxes of that size that could be put in the underground chamber?

Homework Worksheet

10 word problems for students to work on at home. An example problem is provided and explained. Example: Suppose a swimming pool in the shape of a hemisphere is 28m wide. How much water can the pool hold? Round your answers to one decimal place.

10 volume based Word Problems. A math scoring matrix is included. Example: What is the volume of a regular cylinder whose base has radius of 16 cm and has height of 35 cm?

Homework and Quiz Answer Key

Answers for the homework and quiz.

Answers for the lesson and practice sheets.

Find Their Volume....

A mathematician, a physicist, and an engineer are all given identical rubber balls and told to find the volume. They are given anything they want to measure it, and have all the time they need. The mathematician pulls out a measuring tape and records the circumference. He then divides by two times pi to get the radius, cubes that, multiplies by pi again, and then multiplies by four-thirds and thereby calculates the volume. The physicist gets a bucket of water, places 1.00000 gallons of water in the bucket, drops in the ball, and measures the displacement to six significant figures. And the engineer? He writes down the serial number of the ball, and looks it up.

Go Math 5th Grade Chapter 11 Tests - Geometry & Volume - Distance Learning!

• Google Slides™

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What is this product?

★This is a math test designed from the Go Math curriculum for fifth grade. The questions cover all the topics and lessons from the chapter, but are much clearer than the current tests. They are based more on the "on your own" sections from each lesson. They are clear and to the point and use the same format and directions from the program.

What is included in this product?

★THREE tests!!!

★The first test is a PDF file. There are 28 questions covering all the topics from the chapter. An answer key is included.

★The second test is a Google Slides file. It is exactly the same as the pdf file, with modified directions for online work. There are text boxes for students to type in their answers and objects and shapes to manipulate. A separate answer key is included.

★The third test is a Google Form featuring multiple choice and short answer questions. In some cases, the Google Form has slightly fewer questions than the other versions due to the nature of the questions and format of Google Forms. The short answer questions have a variety of acceptable answers based on potential spelling and spacing errors the students may make. This is completely EDITABLE!

What topics does this cover?

★Lesson 1: Polygons

★Lesson 2: Triangles

★Lesson 3: Quadrilaterals

★Lesson 4: Three-Dimensional Figures

★Lesson 5: Investigate • Unit Cubes and Solid Figures

★Lesson 6: Investigate • Understand Volume

★Lesson 7: Investigate • Estimate Volume

★Lesson 8: Volume of Rectangular Prisms

★Lesson 9: Algebra • Apply Volume Formulas

★Lesson 10: Problem Solving • Compare Volumes

★Lesson 11: Find Volume of Composed Figures

A FULL YEAR BUNDLE is also available for purchase at a discounted rate!

Please check out my other Go Math resources for grades 2, 3, and 4!

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