Surface and Area of Pyramids and Cones

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Surface and Area of Pyramids and Cones
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Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
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Warm Up 1. A rectangular prism is 0.6 m by 0.4 m
by 1.0 m. What is the surface area? 2. A
cylindrical can has a diameter of 14 cm and a
height of 20 cm. What is the surface area to the
nearest tenth? Use 3.14 for ?.
2.48 m2
1186.9 cm2
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Problem of the Day Sandy is building a model of a
pyramid with a hexagonal base. If she uses a
toothpick for each edge, how many toothpicks will
she need?
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Learn to find the surface area of pyramids and
cones.
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Vocabulary
slant height regular pyramid right cone
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Regular Pyramid
The slant height of a pyramid or cone is measured
along its lateral surface.
Right cone
The base of a regular pyramid is a regular
polygon, and the lateral faces are all congruent.
In a right cone, a line perpendicular to the base
through the tip of the cone passes through the
center of the base.
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Additional Example 1 Finding Surface Area
Find the surface area of each figure
1 2
A. S B Pl
20.16 ft2
B. S pr2 prl
p(32) p(3)(6)
27p ? 84.8 cm2
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Try This Example 1
Find the surface area of each figure.
1 2
5 m
A. S B Pl
39 m2
3 m
3 m
B. S pr2 prl
18 ft
p(72) p(7)(18)
7 ft
175p ? 549.5 ft2
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Additional Example 2 Exploring the Effects of
Changing Dimensions
A cone has diameter 8 in. and slant height 3 in.
Explain whether tripling the slant height would
have the same effect on the surface area as
tripling the radius.
They would not have the same effect. Tripling the
radius would increase the surface area more than
tripling the slant height.
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Try This Example 2
A cone has diameter 9 in. and a slant height 2
in. Explain whether tripling the slant height
would have the same effect on the surface area as
tripling the radius.
Original Dimensions Triple the Slant Height Triple the Radius

S pr2 pr(3l)
S pr2 prl
S p(3r)2 p(3r)l
p(4.5)2 p(4.5)(2)
p(4.5)2 p(4.5)(6)
p(13.5)2 p(13.5)(2)
29.25p in2 ? 91.8 in2
47.25p in2 ? 148.4 in2
209.25p in2 ? 657.0 in2
They would not have the same effect. Tripling the
radius would increase the surface area more than
tripling the height.
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Additional Example 3 Application
The upper portion of an hourglass is
approximately an inverted cone with the given
dimensions. What is the lateral surface area of
the upper portion of the hourglass?
Pythagorean Theorem
a2 b2 l2
102 262 l2
l ? 27.9
Lateral surface area
L prl
p(10)(27.9) ? 876.1 mm2
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Try This Example 3
A road construction cone is almost a full cone.
With the given dimensions, what is the lateral
surface area of the cone?
Pythagorean Theorem
a2 b2 l2
12 in.
42 122 l2
4 in.
l ? 12.65
Lateral surface area
L prl
p(4)(12.65) ? 158.9 in2
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Lesson Quiz Part 1
Find the surface area of each figure to the
nearest tenth. Use 3.14 for p. 1. the triangular
pyramid 2. the cone
6.2 m2
175.8 in2
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Insert Lesson Title Here
Lesson Quiz Part 2
3. Tell whether doubling the dimensions of a
cone will double the surface area.
It will more than double the surface area because
you square the radius to find the area of the
base.