Vocabulary

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Vocabulary
Volume Volume of Prisms Formula
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Volume is the number of cubic units needed to
fill a space.
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You need 10, or 5 2, centimeter cubes to cover
the bottom of this rectangular prism.
You need 3 layers of 10 cubes each to fill the
prism. It takes 30, or 5 2 3, cubes.
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Volume is expressed in cubic units, so the volume
of the prism is 5 cm 2 cm 3 cm 30 cubic
centimeters, or 30 cm3.
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The volume of a rectangular prism is the area of
its base times its height. This formula can be
used to find the volume of any prism.
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Teacher Example 1 Finding the Volume of a
Rectangular Prism Find the volume of the
rectangular prism.
Step 1 Find the area of the base.
13 in.
11 in.
26 in.
B 26 11
The base is a rectangle.
Multiply.
B 286
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Teacher Example 1 Continued Find the volume of
the rectangular prism.
Step 2 Find the volume.
13 in.
11 in.
26 in.
V Bh
Write the formula.
V 286 13
Substitute for B and h.
Multiply.
V 3,718 in3
The volume of the prism is 3,718 in3.
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Student Practice 1
Find the volume of the rectangular
prism.
Step 1 Find the area of the base.
16 in.
12 in.
29 in.
B 29 12
The base is a rectangle.
Multiply.
B 348
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Student Practice 1 Continued
Find the volume of the rectangular prism.
Step 2 Find the volume.
16 in.
12 in.
29 in.
V Bh
Write the formula.
V 348 16
Substitute for B and h.
Multiply.
V 5,568 in3
The volume of the prism is 5,568 in3.
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You can also use the formula V Bh to find the
volume of a triangular prism. For triangular
prisms, B represents the area of a triangle,
rather than a rectangle.
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Teacher Example 2 Finding the Volume of a
Triangular Prism Find the volume of each
triangular prism. A. Step 1 Find the area of the
base.
Multiply.
B 2.535
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Teacher Example 2A Finding the Volume of a
Triangular Prism Continued Find the volume of
each triangular prism. A. Step 2 Find the volume.
Multiply.
V 10.14 m3
The volume of the prism is 10.14 m3.
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Teacher Example 2B Finding the Volume of a
Triangular Prism Find the volume of each
triangular prism. B. Step 1 Find the area of the
base.
Multiply.
B 22.75
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Teacher Example 2B Finding the Volume of a
Triangular Prism Continued Find the volume of
each triangular prism. B. Step 2 Find the volume.
Multiply.
V 136.5 ft3
The volume of the prism is 136.5 ft3.
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Student Practice 2A Find the volume of each
triangular prism. A. Step 1 Find the area of the
base.
7 m
1.6 m
4.2 m
Multiply.
B 3.36
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Student Practice 2A Continued Find the volume of
each triangular prism. A. Step 2 Find the volume.
7 m
1.6 m
4.2 m
Multiply.
V 23.52 m3
The volume of the prism is 23.52 m3.
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Student Practice 2B Find the volume of each
triangular prism. B. Step 1 Find the area of the
base.
9 ft
5 ft
4.5 ft
Multiply.
B 20.25
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Student Practice 2B Continued
Find the volume of each triangular prism. B.
Step 2 Find the volume.
9 ft
5 ft
4.5 ft
Multiply.
V 101.25 ft3
The volume of the prism is 101.25 ft3.
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Teacher Example 3 Application An artist wants to
make glass paper-weights with the dimensions
shown. He estimates that he will need less than
20 cubic centimeters of glass for each
paperweight. Is his estimate reasonable? Explain.
3 cm
5.2 cm
Step 1 Find the area of the base.
6 cm
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Teacher Example 3 Continued An artist wants to
make glass paper-weights with the dimensions
shown. He estimates that he will need less than
20 cubic centimeters of glass for each
paperweight. Is his estimate reasonable? Explain.
3 cm
5.2 cm
Step 2 Find the volume.
6 cm
No each paperweight will require about 47 cm3 of
glass.
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Student Practice 3 An architect wants to make a
model building with the dimensions shown. He
estimates that he will need more than 60 cubic
centimeters of paper for each building. Is his
estimate reasonable? Explain.
5 cm
5.5 cm
Step 1 Find the area of the base.
6 cm
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Student Practice 3 Continued An architect wants
to make a model building with the dimensions
shown. He estimates that he will need more than
60 cubic centimeters of paper for each building.
Is his estimate reasonable? Explain.
5 cm
5.5 cm
Step 2 Find the volume.
6 cm
No each building will require about 83 cm3 of
paper.
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10.8 Warm-Up
Find the volume of each figure. 1. triangular
prism with a height of 12 cm and a triangular
base with base length 7.3 cm and height 3.5 cm
2. Find the volume of the figure shown.