Name
12.2
?
Understand Volume
Essential Question
Geometry and
Measurement—5.6.A,
5.6.B
MATHEMATICAL PROCESSES
5.1.C, 5.1.D
How can you use unit cubes to find the volume
of a rectangular prism?
Hands
On
Investigate
Investigate
Connect You can find the volume of a rectangular prism by
counting unit cubes. Volume is the measure of the amount of
space a solid figure occupies and is measured in cubic units.
Each unit cube has a volume of 1 cubic unit.
1
2
3
4
5
6
7
8
The rectangular prism above is made up of _ unit cubes
and has a volume of _ cubic units.
Materials ■ rectangular prism net A ■ centimeter cubes
A. Cut out, fold, and tape the net to form a rectangular prism.
B. Use centimeter cubes to fill the base of the rectangular prism
without gaps or overlaps. Each centimeter cube has a length, width,
and height of 1 centimeter and a volume of 1 cubic centimeter.
• How many centimeter cubes make up the length
of the first layer? the width? the height?
length: _ width: _ height: _
• How many centimeter cubes are used to fill the base? _
C. Continue filling the rectangular prism, layer by layer. Count
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the number of centimeter cubes used for each layer.
• How many centimeter cubes are in each layer? _
• How many layers of cubes fill the rectangular prism? _
• How many centimeter cubes fill the prism? _
So, the volume of the rectangular prism is _ cubic centimeters.
Module 12
441
Make
Make Connections
Connections
To find the volume of three-dimensional figures, you measure
in three directions. For a rectangular prism, you measure its
length, width, and height. Volume is measured using cubic
units, such as cubic centimeters or cubic inches. You can also
write these as cu cm or cu in.
1 cu cm
• Which has a greater volume, 1 cu cm or 1 cu in.? Explain.
1 cu in.
Find the volume of the prism if each cube represents 1 cu cm,
1 cu in., and 1 cu ft.
2 units
_ cu cm
_ cu in.
6 units
_ cu ft
3 units
Math Talk
Mathematical Processes
Would the prism above be the
same size if it were built with
centimeter cubes, inch cubes,
or foot cubes? Explain.
Share
Share and
and Show
Show
1.
2.
3 cm
4 in.
4 cm
2 in.
3 in.
Each cube 5 1 cu in.
4 cm
Each cube 5 1 cu cm
Volume = _ cu _
Volume = _ cu _
Compare the volumes. Write <, >, or =.
3.
4 cm
4 cm
Each cube 5 1 cu cm
_ cu cm
442
4 in.
4 in.
Each cube 5 1 cu in.
● _ cu in.
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2 in.
2 cm
Name
Problem
Problem Solving
Solving
4.
Connect What is the relationship among the number of
centimeter cubes you used to fill each layer, the number of layers, and
the volume of the prism on page 441?
5.
If you had a rectangular prism that had a length of 3 units,
a width of 4 units, and a height of 2 units, how many unit cubes would
you need for each layer? How many unit cubes would you need to fill the
rectangular prism?
6.
What’s the Error? Al says that a cube with edges that
measure 10 cm has a volume that is twice as much as a cube with sides
that measure 5 cm. Explain and correct Al’s error.
7.
Pia built a rectangular prism with cubes. The base of her
prism has 12 cm cubes. If the prism was built with 108 cm cubes, what is
the height of her prism?
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8. Multi-Step A packing company makes boxes with edges each
measuring 3 feet. What is the volume of a box? If 10 boxes are put in a
shipping container and completely fill it with no gaps or overlaps, what
is the volume of the shipping container?
Module 12 • Lesson 2
443
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
9. Nabanita needs 140 cubes to make a model. The figure shows
the number of cubes in a box. How many boxes of cubes does
Nabanita need to buy so she has enough cubes for her model?
A
2 boxes
B
3 boxes
C
14 boxes
D
16 boxes
10. A box is filled with speakers. Each speaker has a volume of 1 cubic foot.
Ten speakers can fit in each layer and the height of the box is 4 feet.
What is the volume of the box?
A
40 cubic feet
C
10 cubic feet
B
14 cubic feet
D
20 cubic feet
11. Multi-Step A jewelry box has 3 drawers. Each drawer is 10 inches
long, 5 inches wide, and 6 inches tall. Find the combined volume
of the drawers.
A
11 cu. in.
B
300 cu. in.
C
33 cu. in.
D
900 cu. in.
TEXAS Test Prep
A
25 cubic feet
B
25 cubic meters
C
75 cubic meters
D
75 cubic centimeters
5 cm
3 cm
5 cm
Each cube 5 1 cu cm
444
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12. Find the volume of the rectangular prism.
Geometry and Measurement—5.6.A,
5.6.B
MATHEMATICAL PROCESSES 5.1.C, 5.1.D
H o mewo rk
and Practice
12.2
Name
Understand Volume
1.
2.
2 in.
3 cm
4 in.
6 in.
5 cm
4 cm
Each cube = 1 cu in.
Each cube = 1 cu cm
Volume = _ cu _
Volume = _ cu _
Compare the volumes. Write <, >, or =.
3.
4 in.
4 cm
3 in.
3 cm
3 in.
3 cm
Each cube = 1 cu in.
Each cube = 1 cu cm
_ cu in.
_ cu cm
Problem
Problem Solving
Solving
4. Salim built a rectangular prism with a length
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of 5 inches, a width of 4 inches, and a height
of 3 inches. Would the prism Natalie built with
a length of 3 inches, a width of 4 inches, and a
height of 5 inches have the same volume or a
different volume than Salim’s prism? Explain.
5. Oliver and Layla each built a rectangular prism
with centimeter cubes. Both prisms have a
volume of 24 cubic centimeters, but they do
not look the same. Give possible dimensions
for each prism.
Module 12 • Lesson 2 445
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
6. Find the volume of the rectangular prism.
7. Mason builds a tower with centimeter cubes
3 cm
for his design project. The figure below shows
the part of the tower that he has completed
so far.
4 cm
7 cm
10 cm
Each cube = 1 cu cm
120 cubic inches
B
120 cubic centimeters
C
70 cubic inches
D
70 cubic centimeters
2 cm
3 cm
What does Mason need to do for the tower to
have a volume of 54 cubic centimeters?
8. A chest is filled with toy blocks. Each block has
a volume of 1 cubic foot. Twenty-five blocks fit
in the bottom of the chest and the height of the
chest is 3 feet. What is the volume of the chest?
A
75 cubic feet
C
28 cubic feet
B
60 cubic feet
D
25 cubic feet
10. Multi-Step Lily serves 1-inch cheese cubes to
her guests on a rectangular tray that is 6 inches
long, 4 inches wide, and 2 inches tall. When
the tray is only half full, what is the volume of
the cheese cubes?
446
A
Add one layer of cubes.
B
Add 33 cubes.
C
Add 2 cubes.
D
Add two layers of cubes.
9. Which of the measures below represents the
greatest volume?
A
14 cubic inches
B
14 cubic feet
C
14 cubic centimeters
D
14 cubic meters
11. Multi-Step Fernando builds a rectangular
prism with centimeter cubes. The length of the
prism is 2 centimeters. The width is twice the
length and the height is twice the width. What
is the volume of Fernando’s prism?
A
96 cu in.
C
48 cu in.
A
48 cu cm
C
8 cu cm
B
12 cu in.
D
24 cu in.
B
16 cu cm
D
64 cu cm
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A