lesson 26 find volume using formulas · 2018. 9. 9. · modeled and guided instruction learn about...

Introduction

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Use What You Know

Lesson 26 Find Volume Using Formulas

Lesson 26Find Volume Using Formulas

a. The model has a length of inches and a width of inches.

b. How many cubes are in the top layer of the model?

c. How can you find the number of cubes in the top layer without counting the cubes?

d. How many layers of cubes does the model have?

e. How many cubes are in Becky’s model?

f. Explain how you can find the volume of Becky’s model without counting each cube.

Becky uses 1-inch cubes to create a model for a small paper gift bag she is making. Her model is a rectangular prism. What is the volume of Becky’s model?

In previous lessons, you learned how to find volume by counting unit cubes. In this lesson, you will learn how to find volume using a formula. Take a look at this problem.

5.MD.C.5a

5.MD.C.5b

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Find Out More


Below is a picture of Becky’s gift bag next to her model.

3 in.

2 in.4 in.

Notice that the base of the bag is a rectangle 4 inches long and 2 inches wide. The area of the base is 8 square inches. The height of the bag is 3 inches.

Look at the model. There are 8 cubes in each layer. There are 3 layers of cubes.

Volume 5 length 3 width 3 height

length width height

Volume 5 number of cubes

in each layernumberof layers3

8 33

4 3 2 33

V 5 < 3 w 3 h

Reflect1 The area of the base of the gift bag is the product of the length and width of the bag.

What is the volume of the bag? Explain how you can use the area of the base of the gift bag to find the volume of the bag.

Modeled and Guided Instruction

Learn About


Lesson 26


Using a Formula to Find Volume

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

Gareth has a rectangular pencil cup on his desk. The cup is 3 inches long, 2 inches wide, and 5 inches high. What is the volume of the pencil cup?

Picture It You can picture the pencil cup as a rectangular prism made up of 1-inch cubes.

Model It You can draw a model of the pencil cup and label its dimensions.

3 in.2 in.

5 in.

©Curriculum Associates, LLC Copying is not permitted. 259Lesson 26 Find Volume Using Formulas

Connect It Now you will solve the problem from the previous page using the picture and model of the pencil cup.

2 Explain how you can find the volume of the pencil cup using the picture. Find the volume.

3 Explain how the area of the base of the model of the pencil cup in Model It relates to

the prism in Picture It.

4 Explain how you can find the volume of the pencil cup using the model.

5 Write two different multiplication equations you can use to find the volume of the pencil cup.

6 Explain how you can use the dimensions of a rectangular prism to find its volume.

Try It Use what you just learned about finding volume to solve these problems. Show your work on a separate sheet of paper.

7 What is the volume of a rectangular jewelry box with a length of 8 centimeters, a

width of 5 centimeters, and a height of 4 centimeters?

8 How much space is taken up by a book that is 12 inches long, 10 inches wide, and

1 inch tall?

Guided Practice

Practice


Lesson 26


Example

Using the Formula for Volume

Pair/ShareDid you and your partner solve the problem the same way?

Pair/ShareWhat are some possible dimensions of the base of the box?

9 Evie uses 20 square inches of cardboard for the base of a box. The box has a height of 6 inches. What is the volume of the box?

Show your work.

Solution

Coen is making a clay vase. He wants the interior of the vase to be a rectangular prism with base 3 inches long and 3 inches wide. He wants the vase to hold 45 cubic inches of water. How tall should Coen make the vase?

Look at how you could use a formula to solve the problem.

Volume 5 < 3 w 3 h

45 5 3 3 3 3 h 45 5 9 3 h 45 4 9 5 h

5 5 h

Solution

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

5 inches

The student wrote an equation using the formula for volume. The height is the unknown.

What does 20 square inches represent?


Pair/ShareDoes Danny’s answer make sense?

Pair/ShareHow could you check your answer?

10 The rectangular prism shown below has a volume of 42 cubic meters. What is the length of the prism?

2 m<

3 m

Show your work.

Solution

11 A cube is a rectangular prism whose edge lengths are all the same. What is the volume of a cube with an edge length of 2 feet? Circle the letter of the correct answer.

A 4 cubic feet

B 6 cubic feet

C 8 cubic feet

D 12 cubic feet

Danny chose B as the correct answer. How did he get that answer?

What dimensions are labeled on the prism?

Each side of a cube is a square.

Independent Practice

Practice


Lesson 26


Using the Formula for Volume

Solve the problems.

1 A rectangular prism has a square base with side lengths of 5 centimeters and a height of 7 centimeters. What is the volume of the prism?

A 35 cubic centimeters

B 140 cubic centimeters

C 175 cubic centimeters

D 245 cubic centimeters

2 A rectangular prism has a volume of 100 cubic meters. One of the dimensions is 5 meters. Which could be the other two dimensions of the prism? Circle the letter for all that apply.

A 1 meter, 20 meters

B 5 meters, 10 meters

C 10 meters, 10 meters

D 4 meters, 5 meters

E 20 meters, 20 meters

3 Henry evenly pours 960 cubic inches of sand into the fish tank shown below. Using the guide on the left side of the tank, shade the front of the tank to show how deep the sand is.

15

12

inch

es 9

6

3

040 inches

8 inches

Self Check


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

4 A cardboard box has a volume of 60 cubic feet. Give four different sets of measurements that could be the dimensions of the box.

Show your work.

feet 3 feet 3 feet

feet 3 feet 3 feet

feet 3 feet 3 feet

feet 3 feet 3 feet

5 The number of guppies that a fish tank can safely hold depends on its volume. A fish tank should have a volume of 576 cubic inches to safely hold 3 guppies. How many guppies can a fish tank that is 24 inches long, 12 inches wide, and 16 inches high safely hold?

Show your work.

Answer guppies

lesson 26 find volume using formulas · 2018. 9. 9. · modeled and guided instruction learn about...

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