lesson 27 introduction find volume of composite …...curriculum associates, llc copying is not...

Introduction

©Curriculum Associates, LLC Copying is not permitted.264

Use What You Know

Lesson 27 Find Volume of Composite Figures

Lesson 27Find Volume of Composite Figures

a. Look at the dashed segment in the L-shaped figure. Imagine slicing the solid figure along the dashed line to make two rectangular prisms.

What would be the dimensions of Prism A?

What would be the dimensions of Prism B?

b. How could you find the volume of each rectangular prism?

c. What is the volume of Prism A?

What is the volume of Prism B?

d. How could you find the volume of the L-shaped figure using the two prisms?

e. What is the volume of the L-shaped solid figure?

What is the volume of the L-shaped solid figure below?

6 ftL-shaped Figure Prism A Prism B

4 ft 2 ft

2 ft4 ft

You learned how to use a formula to find the volume of a rectangular prism. In this lesson, you will find the volume of a solid figure made up of more than one rectangular prism. Take a look at this problem.

5.MD.C.5c

©Curriculum Associates, LLC Copying is not permitted. 265Lesson 27 Find Volume of Composite Figures

Find Out More

Rectangles can be combined in different ways to create different two-dimensional shapes. You can find the areas of these shapes by breaking them apart into the rectangles that make them up. There may be more than one way to break apart these shapes.

Rectangular prisms can be combined in different ways to make solid figures. You can find the volume of these solid figures by breaking them apart into the prisms that make them up. There may be more than one way to break apart these solid figures.

Reflect1 Circle one of the solid figures above. Explain how you could find its volume.

Modeled and Guided Instruction

Learn About

©Curriculum Associates, LLC Copying is not permitted.266

Lesson 27

Lesson 27 Find Volume of Composite Figures

Breaking Apart Figures to Find Volume

Read the problem. Then explore how to find the volume of a solid figure by breaking it apart into rectangular prisms in different ways.

Bethany has a raised garden bed. The diagram shows its measurements. All of the corners are right angles. If she fills the bed to the top with soil, how many cubic feet of soil will Bethany need?

Model It You can break the garden bed into two rectangular prisms this way.

6 ft

2 ft4 ft 6 ft

6 ft

2 ft6 1 6 5 12 ft

One rectangular prism measures 6 feet 3 4 feet 3 2 feet.

The other rectangular prism measures 12 feet 3 6 feet 3 2 feet.

Model It You can also break the garden bed into two rectangular prisms in a different way.

6 ft

2 ft4 ft 6 ft

6 ft

2 ft6 1 4 5 10 ft

One rectangular prism measures 6 feet 3 10 feet 3 2 feet.

The other rectangular prism measures 6 feet 3 6 feet 3 2 feet.

6 ft

2 ft4 ft 6 ft

6 ft


Connect It Now you will solve the problem from the previous page using the formula for volume of a rectangular prism.

2 Look at the first model. How can you find the volume of each rectangular prism?

3 How can you find the volume of the entire garden bed?

4 What is the volume of the entire garden bed? Show your work.

5 Now look at the second model. Show how to find the volume of the garden bed if you break it apart this way.

6 Do you need to break apart a solid figure in a certain way to find its volume? Use the problem from the previous page to explain your reasoning.

Try It Use what you just learned about breaking apart solid figures to solve these problems. Show your work on a separate sheet of paper.

7 The Recreation Center has an L-shaped pool. One part of the pool is 8 meters by 6 meters. The other part is 12 meters by 6 meters. The whole pool is 4 meters deep. What is the volume of the entire pool?

8 What is the volume of the solid figure below?

8 ft

6 ft

4 ft

2 ft

3 ft

Guided Practice

Practice

©Curriculum Associates, LLC Copying is not permitted.268 Lesson 27 Find Volume of Composite Figures

Lesson 27

Example

Finding the Volume of Composite Figures

Pair/ShareCould you break apart the solid figure in a different way?

Pair/ShareCan you solve the problem in a different way?

Would it help to draw a diagram to represent the problem?

The student drew a dashed segment to show how to break apart the solid figure.

9 Tia made a two-layer cake. Each layer is a rectangular prism that is 2 inches high. The base of the bottom layer is 100 square inches. The base of the top layer is 64 square inches. What is the total volume of the cake?

Show your work.

Solution

Adam drew a model of a flowerpot. All of its edges meet at right angles. What is the volume of the flowerpot?

Look at how you could break

apart the figure into two

rectangular prisms.30 cm

30 cm

20 cm

20 cm

30 cm

10 cm

10 3 30 3 30 5 9,000 20 3 30 3 20 5 12,000

9,000 1 12,000 5 21,000

Solution

30 cm

30 cm20 cm

10 cm

30 cm

Study the example below. Then solve problems 9–11.

21,000 cubic centimeters


Pair/ShareDoes Kali’s answer make sense?

Pair/ShareHow did you and your partner decide how to break apart the solid figure?

After I break apart the figure, how will I find the missing measurements?

What is the total height of the display?

10 The diagram shows the dimensions of a cement walkway, where all of the sides meet at right angles. What is the total volume of cement needed to make the walkway?

2 ft

10 ft

1 ft

2 ft

8 ft

Show your work.

Solution

11 A candy store is building a display with two rectangular prisms. The base of each prism is a square with a edge length of 5 inches. One prism is 12 inches tall and the other is twice as tall. The two prisms are stacked so that the pieces do not overlap. What is the total volume of the display?

A 36 cubic inches

B 60 cubic inches

C 180 cubic inches

D 900 cubic inches

Kali chose A as the correct answer. How did she get that answer?

Independent Practice

Practice

©Curriculum Associates, LLC Copying is not permitted.270 Lesson 27 Find Volume of Composite Figures

Lesson 27

Finding the Volume of Composite Figures

Solve the problems.

1 A pool shaped like a rectangular prism is 40 feet long, 20 feet wide, and 4 feet deep. Attached to the side of the pool is a hot tub with 1 ·· 4 the volume of the pool. What is the total volume of the pool and hot tub?

A 800 cubic feet

B 1,000 cubic feet

C 3,200 cubic feet

D 4,000 cubic feet

2 The diagram below shows the measurements of a mold used to make sandcastles. Which expression can be used to find the volume of the mold, in cubic inches? Circle the letter for all that apply.

6 in.

7 in.

5 in.

3 in.

2 in.

A (2 3 5 3 3) 1 (5 3 5 3 3)

B (2 3 5 3 3) 1 (7 3 5 3 3)

C (2 3 5 3 6) 1 (5 3 5 3 3)

D (2 3 5 3 6) 1 (7 3 5 3 3)

E (2 3 5 3 3) 1 (7 3 5 3 6)

Self Check


Go back and see what you can check off on the Self Check on page 211.

3 The diagram below shows the dimensions of two identical rectangular prisms joined together.

5 m

11 m

10 m

What is the combined volume of the two prisms? cubic meters

4 Rami designed a small pond for a restaurant. The diagram below shows the measurements of the pond. How many cubic feet of water are needed to fill the pond?

12 ft

2 ft

6 ft

18 ft

4 ft

Show your work.

Answer cubic feet

lesson 27 introduction find volume of composite …...curriculum associates, llc copying is not...

Documents