Name_____________________________________ Class____________________________ Date________________
Lesson 11-5
Volumes of Pyramids and Cones
Lesson Objectives
1 Find the volume of a pyramid
2 Find the volume of the cone
NAEP 2005 Strand: Measurement
Topic: Measuring Physical Attributes
Local Standards: ____________________________________
Key Concepts.
Theorem 11-8: Volume of a Pyramid
and the
.
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The volume of a pyramid is one third the product of the
h
V
B
Theorem 11-9: Volume of a Cone
The volume of a cone is one third the product of the
and the
.
h
V 13Bh, or V r
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B
Examples.
1 Finding Volume of a Pyramid Find the volume of a square pyramid with
base edges 15 cm and height 22 cm.
Because the base is a square, B V5
13
.
Use the formula for volume of a pyramid.
(
)(
V5
)
Substitute
Geometry Lesson 11-5
for B and
for h.
Simplify.
The volume of the square pyramid is
218
?
cm3.
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2 Finding Volume of a Pyramid Find the volume of a
square pyramid with base edges 16 m and slant height 17 m.
17 m
The altitude of a right square pyramid intersects the base
at the center of the square. Because each side of the square
base is 16 m, the leg of the right triangle along the base is
m, as shown.
h
16 m
16 m
17 m
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h
8m
Step 1 Find the height of the pyramid.
172 5 82 1 h2
Use the
289 5 64 1 h2
Simplify.
5 h2
.
Subtract
h5
from each side.
Find the square root of each side.
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Step 2 Find the volume of the pyramid.
Use the formula for
the volume of a pyramid.
V5
5 13
(
)
?
Substitute.
5
Simplify.
m3.
The volume of the square pyramid is
3 Finding Volume of an Oblique Cone Find the volume
of the oblique cone in terms of π.
r5
5
in.
11 in.
V5
5 13 p(
Use the formula for the volume of a cone.
)(
2
)
5
The volume of the cone is
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Substitute
for r and
for h.
6 in.
Simplify.
in.3.
Geometry Lesson 11-5
219
Name_____________________________________ Class____________________________ Date ________________
Quick Check.
1. Find the volume of a square pyramid with base edges 24 m and slant height 13 m.
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2. Find the volume of each cone in terms of π and also rounded as indicated.
a. to the nearest cubic meter
12 m
6m
42 mm
21 mm
3. A small child’s teepee is 6 ft tall and 7 ft in diameter. Find the volume of the
teepee to the nearest cubic foot.
220
Geometry Lesson 11-5
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b. to the nearest cubic millimeter