Name
Class
Date
Lesson 9-2 Volumes of Prisms and Cylinders
Lesson Objective
Common Core Standards
To find the volumes of prisms and
cylinders
Geometry: 8.G.7, 8.G.9
Vocabulary and Key Concepts
The volume V of a prism is the product of the base area B
and the height h.
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Volume of Prisms and Cylinders
h
B
V 5 Bh
B
The volume V of a cylinder is the product of the base area B
and the height h.
V 5 Bh
r
h
Integers are the number of unit cubes, or cubic units, needed to fill a solid.
Examples
1 Finding Volume of a Triangular Prism Find the volume
of this prism.
2 cm
Step 1 Find the area B of the base.
B
1
2
bh
1
2 ?
d Use the triangle area formula.
3.5
?
2
3.5
d
Substitute
3.5
substitute
2
4 cm
3.5 cm
for b. For h,
, the height of the triangle.
d Multiply.
The area of the base is
3.5
cm2.
Step 2 Use the base area to find the volume.
d Use the prism volume formula.
Bh
V
3.5
?
4
14
d
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Course 3 Lesson 9-2
3.5
the height of the
for B. For h, substitute
prism
4
,
.
d Multiply.
The volume of the prism is 14
88
Substitute
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cm3.
Daily Notetaking Guide
10/10/12 4:43 PM
Name
Class
Date
2 Finding Volume of a Cylinder Find the volume of a cylindrical cake that is
5 in. tall with a diameter of 15 in. Give your answer to the nearest cubic inch.
Estimate Use 3 for p. The area of the base is about 3 3 64 in.2, or 192 in.2.
The volume is about 190 3 5 in.3, or 192 in.3.
Step 1 Find the area of the base.
B
r2
56.25p
56.25p
d Substitute. S
d Simplify.
<
S
?
5
883.5729338
The volume of the cylindrical
3
cake is about
884 in. .
The base area is
2
in. .
56.25p
Bh
V
( 7.52 )
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Step 2 Use the base area to
find the volume.
Check for Reasonableness The answer 884 is close to the estimate of 950 .
The answer is reasonable.
Quick Check
1. Find the volume of the prism.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
3.5 ft
52.5 ft3
6 ft
2.5 ft
2. a. Estimation Estimate the volume of the cylinder at the right. Use 3 for p.
B N 3 3 7.52
5 168.75
N 170 mm2
V N 170 3 12
5 2,040 mm3
15 mm
b. Find the volume of the cylinder to the nearest cubic millimeter.
12 mm
7.52 3 p 3 12 5 2,121 mm3
Daily Notetaking Guide
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89
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