Name
12.3
?
Geometry and
Measurement—5.6.B
Also 5.4.G
MATHEMATICAL PROCESSES
5.1.F, 5.1.G
Volume of
Rectangular Prisms
Essential Question
How can you find the volume of a rectangular prism?
Connect The base of a rectangular prism is a rectangle. You know
that area is measured in square units and that the area of a rectangle
can be found by multiplying the length and the width.
Volume is measured in cubic units, such as cubic feet or cu ft. When
you build a prism and add each layer of cubes, you are adding a third
dimension, height.
The area of the base
is _ sq units.
Unlock
Unlock the
the Problem
Problem
Sid built the rectangular prism shown at the right, using 1-inch
cubes. The prism has a base that is a rectangle and has a height of
4 cubes. What is the volume of the rectangular prism that Sid built?
112
112
You can find the volume of a prism in cubic units by multiplying
the number of square units in the base shape by the number of
layers, or its height.
112
Each layer of Sid’s rectangular prism
12
is composed of _ inch cubes.
Height (in layers)
1
2
Volume (in cubic inches)
12
24
3
4
Multiply the height by _.
1. How does the volume change as each layer is added?
© Houghton Mifflin Harcourt Publishing Company
2. What does the number you multiply the height by represent?
So, the volume of Sid’s rectangular prism is _ cu in.
Module 12
447
Share
Share and
and Show
Show
Find the volume.
1. The length of the rectangular prism is __.
5 cm
The width is __. So, the area of the base is __.
4 cm
The height is __. So, the volume of the prism is __.
2.
2 cm
3.
3 ft
3 ft
4 ft
Volume: __
2 in.
5 in.
2 in.
Volume: __
Math Talk
Mathematical Processes
Problem
Problem Solving
Solving
4. Explain what else you need to know to find the volume of a rectangular
How many more layers should
be added to the prism in
Exercise 3 so that the volume
of the prism is 60 cubic
inches? Explain.
5.
Reasoning How can you find the volume of a cube if you
know the area of the base is 25 sq cm?
6.
The volume of a rectangular prism is 40 cu ft. The height
of the prism is 10 ft. What is the area of the base of the prism? Explain.
448
© Houghton Mifflin Harcourt Publishing Company
prism if you know the area of the base.
Name
Problem
Problem Solving
Solving
7. Kayan is designing a box for sugar cubes. Each sugar cube has a volume
of 1 cubic inch. Kayan wants to have 12 cubes in each layer. If he wants
to fit 60 cubes in each box, how tall should the box be?
8.
Multi-Step Golf balls are
packed in cardboard boxes that are 2 inches long,
2 inches wide, and 2 inches high. The boxes are
then packed into larger containers that are
20 inches long, 30 inches wide, and 20 inches high.
How many golf balls can fit in the larger container?
2 in.
20 in.
30 in.
20 in.
9. Multi-Step Yvette uses centimeter cubes to make a bed for her doll.
The bed is in the shape of a rectangular prism. She wants the length of
the prism to be 15 cm. The width should be 5 cm and the height 5 cm.
How many centimeter cubes does Yvette need?
© Houghton Mifflin Harcourt Publishing Company
10.
Multi-Step Cameron uses a rectangular baking pan with
a base measuring 12 square inches. Cameron pours batter in the pan so
that it is 2 inches deep. The finished cake will be 3 times as tall as the batter.
What is the volume of the cake?
Module 12 • Lesson 3
449
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
11. A cube-shaped block of cheese has side lengths of 6 inches. The block
of cheese is cut into smaller pieces. Each piece has a volume of 1 cubic
inch. How many pieces of cheese will there be?
A
18 pieces
B
36 pieces
C
216 pieces
D
72 pieces
12. Frank is packing cube-shaped containers into large boxes. He can fit
15 containers in each layer. If he stacks 8 layers into one box, what is the
volume of the box?
A
64 cubes
C
128 cubes
B
120 cubes
D
256 cubes
13. Multi-Step A rectangular block of cheese has a length of 8 centimeters,
a width of 4 centimeters, and a height of 3 centimeters. If the block is cut
into two equal pieces, what will be the volume of each piece?
A
15 cubic cm
B
28 cubic cm
C
48 cubic cm
D
96 cubic cm
TEXAS Test Prep
A
28 sq cm
B
140 sq cm
C
28 cu cm
D
450
140 cu cm
5 cm
4 cm
7 cm
© Houghton Mifflin Harcourt Publishing Company
14. What is the volume of the rectangular prism at the right?
Geometry and Measurement—5.6.B
Also 5.4.G
MATHEMATICAL PROCESSES 5.1.F, 5.1.G
H o mewo rk
and Practice
12.3
Name
Volume of Rectangular Prisms
Find the volume.
1.
2.
2 ft
3 cm
3 ft
2 cm
8 ft
5 cm
Volume: __
Volume: __
3.
4.
5 cm
6 in.
3 cm
2 in.
2 in.
3 cm
Volume: __
5.
Volume: __
6.
4 in.
4 ft
3 ft
5 in.
3 in.
2 ft
Volume: __
Volume: __
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
7. Vijay has a collection of 50 number cubes that
are each 1 cubic inch. He finds a box that is
4 inches high. He fits 12 cubes into the bottom
of the box. Can Vijay fit all his number cubes
into the box? Explain.
8. Maya wants to use 1-centimeter cubes to
make a larger cube with side lengths of
3 centimeters. How many 1-centimeter
cubes will Maya need?
Module 12 • Lesson 3 451
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
shown below?
5 in.
2 in.
6 in.
A
12 sq in.
B
60 sq in.
C
12 cu in.
D
60 cu in.
11. Jaden fills a box with 32 cubes. The box is
4 cubes long and 2 cubes wide. How many
layers of cubes are in the box?
A
3
B
4
C
8
D
5
13. Multi-Step The shipping clerk packs a cube
with side lengths of 8 inches into a box with
side lengths of 10 inches. What is the volume
of the space left in the larger box for packing
materials?
452
A
598 cubic inches
B
1,000 cubic inches
C
512 cubic inches
D
488 cubic inches
10. Miranda packs cube-shaped jewelry boxes
into a display box that is a rectangular prism.
In the bottom layer, she can fit 4 rows of
7 jewelry boxes. If she stacks 6 layers into the
display box, what is the volume of the
display box?
A
168 cubes
B
28 cubes
C
196 cubes
D
66 cubes
12. Javier has forty 1-centimeter cubes. He builds
a rectangular prism with 6 cubes in the bottom
layer. He wants to have the fewest cubes left
over. How many layers can Javier make?
A
7
B
5
C
6
D
8
14. Multi-Step The volume of cube A is 64 cubic
feet. What is the volume of cube B if its side
lengths are half the length of cube A’s sides?
A
8 cubic feet
B
32 cubic feet
C
16 cubic feet
D
4 cubic feet
© Houghton Mifflin Harcourt Publishing Company
9. What is the volume of the rectangular prism