10-8 Volume of Prisms
California
Standards
MG1.3 Know and use the formulas for
the volume of triangular prisms and
cylinders (area of base × height); compare
these formulas and explain the similarity
between them and the formula for the
volume of a rectangular solid.
Also covered: AF3.1, AF3.2
Holt CA Course 1
10-8 Volume of Prisms
Vocabulary
Volume
Volume of Prisms Formula
Holt CA Course 1
10-8 Volume of Prisms
Volume is the number of cubic
units needed to fill a space.
Holt CA Course 1
10-8 Volume of Prisms
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.
Holt CA Course 1
10-8 Volume of Prisms
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.
Holt CA Course 1
10-8 Volume of Prisms
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.
Holt CA Course 1
10-8 Volume of Prisms
Teacher Example 1: Finding the Volume of a
Rectangular Prism
Find the volume of the rectangular prism.
13 in.
26 in.
11 in.
Step 1: Find the
area of the base.
B = 26 · 11
The base is a rectangle.
B = 286
Multiply.
Holt CA Course 1
10-8 Volume of Prisms
Teacher Example 1 Continued:
Find the volume of the rectangular prism.
13 in.
26 in.
V = Bh
V = 286
11 in.
Step 2: Find the
volume.
Write the formula.
•
13
V = 3,718 in3
Substitute for B and h.
Multiply.
The volume of the prism is 3,718 in3.
Holt CA Course 1
10-8 Volume of Prisms
Student Practice 1:
Find the volume of the rectangular prism.
16 in.
29 in.
12 in.
Step 1: Find the
area of the base.
B = 29 · 12
The base is a rectangle.
B = 348
Multiply.
Holt CA Course 1
10-8 Volume of Prisms
Student Practice 1 Continued:
Find the volume of the rectangular prism.
Step 2: Find the
volume.
16 in.
29 in.
V = Bh
V = 348
12 in.
Write the formula.
•
16
V = 5,568 in3
Substitute for B and h.
Multiply.
The volume of the prism is 5,568 in3.
Holt CA Course 1
10-8 Volume of Prisms
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.
Holt CA Course 1
10-8 Volume of Prisms
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.
1
__
B = ( • 3.9
2
B = 2.535
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•
1.3)
The base is a triangle.
Multiply.
10-8 Volume of Prisms
Teacher Example 2A: Finding the Volume of a
Triangular Prism Continued
Find the volume of each triangular prism.
A. Step 2: Find the volume.
V = Bh
V = 2.535
Write the formula.
•
4
V = 10.14 m3
Substitute for B and h.
Multiply.
The volume of the prism is 10.14 m3.
Holt CA Course 1
10-8 Volume of Prisms
Caution!
The height of a prism is the distance
between its two bases.
Holt CA Course 1
10-8 Volume of Prisms
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.
1
__
B = ( • 6.5
2
B = 22.75
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•
7)
The base is a triangle.
Multiply.
10-8 Volume of Prisms
Teacher Example 2B: Finding the Volume of a
Triangular Prism Continued
Find the volume of each triangular prism.
B. Step 2: Find the volume.
V = Bh
V = 22.75
Write the formula.
•
6
V = 136.5 ft3
Substitute for B and h.
Multiply.
The volume of the prism is 136.5 ft3.
Holt CA Course 1
10-8 Volume of Prisms
Student Practice 2A:
Find the volume of each triangular prism.
A. Step 1: Find the area of the base.
7m
1.6 m
4.2 m
1
__
B = ( • 4.2
2
B = 3.36
Holt CA Course 1
•
1.6)
The base is a triangle.
Multiply.
10-8 Volume of Prisms
Student Practice 2A Continued:
Find the volume of each triangular prism.
A. Step 2: Find the volume.
7m
1.6 m
4.2 m
V = Bh
V = 3.36
Write the formula.
•
7
V = 23.52 m3
Substitute for B and h.
Multiply.
The volume of the prism is 23.52 m3.
Holt CA Course 1
10-8 Volume of Prisms
Student Practice 2B:
Find the volume of each triangular prism.
B. Step 1: Find the area of the base.
9 ft
4.5 ft
1
__
B = ( • 4.5
2
B = 20.25
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•
9)
5 ft
The base is a triangle.
Multiply.
10-8 Volume of Prisms
Student Practice 2B Continued:
Find the volume of each triangular prism.
B. Step 2: Find the volume.
9 ft
4.5 ft
V = Bh
V = 20.25
•
5
V = 101.25 ft3
5 ft
Write the formula.
Substitute for B and h.
Multiply.
The volume of the prism is 101.25 ft3.
Holt CA Course 1
10-8 Volume of Prisms
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.
5.2 cm
3 cm
6 cm
Step 1: Find the area of the base.
1
__
The base is a triangle.
B=
• 6 • 5.2 = 15.6
2
Holt CA Course 1
10-8 Volume of Prisms
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.
Step 2: Find the volume.
V = Bh
3 cm
5.2 cm
6 cm
Write the formula.
V = 15.6 • 3 = 46.8 cm3 Substitute for B and h.
No; each paperweight will require about 47 cm3 of
glass.
Holt CA Course 1
10-8 Volume of Prisms
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.
5.5 cm
5 cm
6 cm
Step 1: Find the area of the base.
1
The base is a triangle.
B = __ • 6 • 5.5 = 16.5
2
Holt CA Course 1
10-8 Volume of Prisms
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.
Step 2: Find the volume.
6 cm
V = Bh
V = 16.5
5 cm
5.5 cm
Write the formula.
•
5 = 82.5 cm3 Substitute for B and h.
No; each building will require about 83 cm3 of paper.
Holt CA Course 1
10-8 Volume of Prisms
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.
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