Surface Area of Prisms and Cylinders

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6-8
Surface Area of Prisms and Cylinders
Warm Up
Problem of the Day
Lesson Presentation
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Warm Up 1. A triangular pyramid has a base area
of 1.2 m2 and a height of 7.5 m. What is the
volume of the pyramid? 2. A cone has a radius
of 4 cm and a height of 10 cm. What is the volume
of the cone to the nearest cubic centimeter? Use
3.14 for p.
3 m3
167 cm3
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Problem of the Day An ice cream cone is filled
halfway to the top. The radius of the filled part
is half the radius at the top. What fraction of
the cones volume is filled?
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Learn to find the surface area of prisms and
cylinders.
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Vocabulary
surface area lateral face lateral surface
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Surface area is the sum of the areas of all
surfaces of a figure. The lateral faces of a
prism are parallelograms that connect the bases.
The lateral surface of a cylinder is the curved
surface.
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Additional Example 1 Finding Surface Area
Find the surface area of each figure
A. S 2pr2 2prh
2p(42) 2p(4)(6)
80p in2 ? 251.2 in2
B. S 2B Ph
204 ft2
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Try This Example 1
Find the surface area of each figure
15 cm
A. S 2pr2 2prh
3 cm
2p(152) 2p(15)(3)
540p in2 ? 1695.6 cm2
7 cm
7 cm
6 cm
B. S 2B Ph
10 cm
7 cm
252 cm2
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Additional Example 2 Exploring the Effects of
Changing Dimensions
A cylinder has diameter 8 in. and height 3 in.
Explain whether tripling the 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 height.
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Try This Example 2
A cylinder has diameter 6 in. and height 2 in.
Explain whether doubling the height would have
the same effect on the surface area as doubling
the radius.
Original Dimensions Double the Height Double the Radius

S 2pr2 2pr(2h)
S 2pr2 2p(2r)h
S 2pr² 2prh
2p(3)2 2p(3)(4)
2p(6) 2 2p(3)(2)
2p(3)2 2p(3)(2)
42p in2 131.88 in2
84p in2 263.76 in2
30p in2 94.2 in2
They would not have the same effect. Doubling the
radius would increase the surface area more than
doubling the height.
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Additional Example 3 Application
A cylindrical soup can is 7.6 cm in diameter and
11.2 cm tall. What is the area of the label that
covers the side of the can?
Only the lateral surface needs to be covered.
L 2?rh
2?(3.8)(11.2)
The diameter is 7.6 cm, so r 3.8 cm.
267.3 cm2
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Try This Example 3
A cylindrical storage tank that is 6 ft in
diameter and 12 ft tall needs to be painted. The
paint will cover 100 square feet per gallon. How
many gallons will it take to paint the tank?
S 2?r2 2?rh
The diameter is 6 ft, so r 3 ft.
2?(32) 2?(3)(12)
282.6 ft2
Move the decimal point 2 places to the left to
divide by 100.
2.826 gal
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Lesson Quiz
Find the surface area of each figure to the
nearest tenth. Use 3.14 for p. 1. the triangular
prism 2. the cylinder
360 cm2
320.3 in2
3. All outer surfaces of a box are covered with
gold foil, except the bottom. The box measures 6
in. long, 4 in. wide, and 3 in. high. How much
gold foil was used?
84 in2