Download 11-3 - Ithaca Public Schools

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Lesson 11-3
Surface Areas of Pyramids and Cones
Lesson Objectives
1 Find the surface area of a pyramid
2 Find the surface area of a cone
NAEP 2005 Strand: Measurement
Topic: Measuring Physical Attributes
Local Standards: ____________________________________
Theorem 11-3: Lateral and Surface Area of a Regular Pyramid
The lateral area of a regular pyramid is half the product of the
and the
.
L.A. B
The surface area of a regular pyramid is the sum of the
and the
.
Theorem 11-4: Lateral and Surface Area of a Cone
The lateral area of a right cone is half the product of the
and the
.
B
L.A. 12 ? 2πr ? , or L.A. r
The surface area of a right cone is the sum of the lateral area and the area of the base.
S.A. A regular pyramid is
The altitude of a pyramid or a cone is
The height of a pyramid or a cone is
edge
Lateral face
The slant height of a regular pyramid is
Base
The lateral area of a pyramid is
edge
Regular Pyramid
The surface area of a pyramid is
212
Geometry Lesson 11-3
Daily Notetaking Guide
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S.A. All rights reserved.
Vocabulary and Key Concepts.
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A right cone is
The slant height of a cone is
/
h
r
The lateral area of a cone is
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The surface area of a cone
cone
Examples.
1 Finding Surface Area of a Pyramid Find the surface area of a square
pyramid with base edges 7.5 ft and slant height 12 ft.
12 ft
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7.5 ft
The perimeter p of the square base is 4 You are given find the lateral area.
ft and you found that p L.A. 5
L.A. 5 12
ft, or
ft.
ft, so you can
Use the formula for lateral area of a pyramid.
(
)(
)
L.A. 5
Substitute.
Simplify.
Find the area of the square base.
Because the base is a square with side length 7.5 ft,
B s2 S.A. 5
S.A. 5
2
1
.
Use the formula for surface area of a pyramid.
1
S.A. 5
Substitute.
Simplify.
The surface area of the square pyramid is
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ft2.
Geometry Lesson 11-3
213
Name_____________________________________ Class____________________________ Date ________________
2 Finding Lateral Area of a Cone Leandre uses paper cones to cover her
plants in the early spring. The diameter of each cone is 1 ft, and its height is
1.5 ft. How much paper is in the cone? Round your answer to the nearest
tenth.
Use the formula L.A. to find the lateral area of the cone.
ft.
The cone’s diameter is 1 ft, so its radius r is
2
2
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The altitude of the cone, radius of the base, and slant height form a
triangle. Use the
to find the slant height .
Find the lateral area.
L.A. 5
Use the formula for lateral area of a cone.
(
L.A. 5 p
)
L.A. <
Substitute
for r and
for .
Use a calculator.
The lateral area of the cone is about
ft2.
Quick Check.
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1. Find the surface area of a square pyramid with base edges 5 m and slant
height 3 m.
2. Find the lateral area of a cone with radius 15 in. and height 20 in. to the
nearest square inch.
214
Geometry Lesson 11-3
Daily Notetaking Guide