Lesson 25 Introduction Find Volume Using Unit Cubes · 2018-09-09 · Modeled and Guided...

Introduction

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Use What You Know

Lesson 25 Find Volume Using Unit Cubes

Lesson 25Find Volume Using Unit Cubes

a. How many cubes are in the bottom layer of the box?

b. How many cubes are in each layer?

c. How many layers of cubes are in the box?

d. Should Carl use square units or cubic units to find the volume of the box? Explain.

e. Describe how Carl can find the volume, including what unit he should use.

Carl filled the clear box shown below with unit cubes to find its volume.

3 ft

2 ft

1 ft

What is the volume of the box?

In Lesson 24, you learned that you can fill a solid figure with unit cubes to find its volume. Now take a look at this problem.

5.MD.C.4

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Volume is measured in cubic units.

The size of the cubic units used to measure volume can be based on the units used to measure edge lengths. For example, the box on the previous page has edge lengths measured in feet, so its volume is most easily measured in cubic feet.

Each unit cube used to pack the box is 1 foot long, 1 foot wide, and 1 foot high.

1 ft

1 ft 1 ft

Volume 5 1 cubic foot

One way to find the volume of the box is to count how many cubes fill the box. There are a total of 6 cubes in the box. Each cube has a volume of 1 cubic foot. So, the volume of the box is 6 cubic feet.

Here are two other units you might use to measure volume.

Units of Volume cubic inch cubic centimeter

Unit Cube1 in.

1 in. 1 in.

1 cm

1 cm 1 cm

Reflect1 Suppose Carl’s box was 4 feet high instead of 2 feet. What would be its volume?

Explain your reasoning.

Modeled and Guided Instruction

Learn About


Lesson 25


Finding the Volume of a Rectangular Prism

Read the problem below. Then explore different ways to find the volume of a rectangular prism.

Abigail used cardboard to build a rectangular prism like the one shown below.

4 cm2 cm

3 cm

What is the volume of the prism?

Picture It You can find the volume of the prism by filling it with unit cubes and counting the number of cubes.

2 cm

3 cm

4 cm

Use cubes that are each 1 cubic centimeter. 24 cubes fill the rectangular prism.

Model It You can also find the volume by counting the number of cubes in one layer and multiplying by the number of layers.

one layer 3 layers

Use cubes that are each 1 cubic centimeter. There are 8 cubes in each layer and 3 layers.

8 cubes 3 3 layers 5 24 cubes


Connect It Now you will solve the problem from the previous page by multiplying.

2 Look at the models on the previous page. How could you find the number of cubes in

one layer without counting the cubes?

3 Once you know how many cubes are in one layer, what else do you need to know to

find the volume?

4 Since there are 8 cubes in each layer, and you know there are 3 layers, what

multiplication expression can you write to find the volume of the prism?

5 What is the volume of Abigail’s rectangular prism?

6 Explain how you can use multiplication to find the volume of any rectangular prism.

Try It Use what you just learned about ways to find the volume of a rectangular prism to solve these problems. Show your work on a separate sheet of paper.

7 What is the volume of the rectangular prism below?

3 in.3 in.

3 in.

8 Mr. Wong filled the figure below with 1-foot unit cubes to find its volume.

2 ft

2 ft

1 ft

What is the volume of Mr. Wong’s figure?

Guided Practice

Practice


Lesson 25

Finding Volume Using Unit Cubes


Example

Pair/ShareCould you solve this problem another way?

Pair/ShareCan you usemultiplication to solvethis problem?

How many layers of cubes will there be in the box?

The student started by finding the number of cubes in the bottom layer.

9 A box measures 6 centimeters long, 2 centimeters wide, and 4 centimeters high. What is the volume of the box?

4 cm

2 cm 6 cm

Show your work.

Solution

Pedro has a storage box with a volume of 36 cubic feet. He knows that the box is 4 feet long and 3 feet wide. How high is the box?

Look at how you could show your work using a drawing and multiplication facts.

3 ft4 ft

3 3 4 5 12

12 3 5 36

5 36 4 12

5 3

Solution

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

3 feet


Pair/ShareDoes Nam’s answer make sense?

Pair/ShareHow did you decide which method to use to solve the problem?

How many cubes are there in each layer?

There is more than one way to find the volume of a rectangular prism.

10 Kamala made the figure below using cubes.

2 in.

3 in.

5 in.

What is the volume of Kamala’s figure?

Show your work.

Solution

11 What is the volume of the rectangular prism below?

6 ft1 ft

1 ft

A 6 square feet

B 6 cubic feet

C 8 square feet

D 8 cubic feet

Nam chose D as the correct answer. How did he get that answer?

Independent Practice

Practice


Lesson 25

Finding Volume Using Unit Cubes


Solve the problems.

1 How many cubes are in the bottom layer of the rectangular prism below?

A 3

B 6

C 12

D 24

2 Which expressions can be used to find the volume of the rectangular prism below? Circle the letter for all that apply.

4 ft

6 ft5 ft

A 30 3 4

B (5 1 6) 3 4

C 30 1 30 1 30 1 30

D 5 1 6 1 4

E 30 1 4

3 Flora has a rectangular gift box that has a volume of 24 cubic inches. The box is 2 inches tall. What could be the length and width of the box? Select Yes or No for each length and width.

a. 11 inches long, 11 inches wide

Yes No

b. 4 inches long, 3 inches wide

Yes No

c. 2 inches long, 10 inches wide

Yes No

d. 6 inches long, 2 inches wide

Yes No

e. 1 inch long, 12 inches wide

Yes No

Self Check


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

4 Both figures are filled with unit cubes of the same size. Which rectangular prism has the larger volume, figure A or figure B?

Show your work.

Answer has the larger volume.

5 Mato drew the rectangular prism shown below.

4 cm

2 cm 5 cm

Part A Draw and label a different rectangular prism with the same volume as Mato’s prism.

Part B Explain how you know that the volume of your prism is the same as the volume of Mato’s prism.

A B

Lesson 25 Introduction Find Volume Using Unit Cubes · 2018-09-09 · Modeled and Guided...

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