9.7 Surface Area

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9.7 Surface Area

• Geometry CP
• Chapter 9 Area

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Surface Area

• Surface area applies to solids such as prisms,
  pyramids, cylinders and cones (think 3-D object)
• The surface area is the sum of the areas of all
  the faces or surfaces that enclose the solid.
  This includes the top and bottom (bases) and its
  remaining surfaces (lateral faces or surfaces)

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Surface Area

• Prism

Surface area
Sum of all faces
h
2(b1b2) 2(b1h) 2(b2h)
b2
b1
Ex A skyscraper
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Prism Example

• Find the surface area of the prism

Surface area
2cm
5cm
2(4)(5) 2(4)(2) 2(5)(2)
4cm
40 16 20
76
Surface area 76 cm2
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Surface Area

• Pyramid

Surface area
Triangular faces base
(lateral faces)
h
b
Where n triangular faces h slant height h2
height of base
Ex Great Pyramid at Giza
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Pyramid Example

• Find the surface area of the square-based pyramid.

Surface area
192 144
336
Surface area 336 cm2
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Surface Area

• Cylinder

Surface area
2 circles (bases) lateral surface
2?r2 2?rh (where h height of cylinder and
the base of the lateral surface is the
circumference of circular base 2?r)
Example Soda can
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Cylinder Example

• Find the surface area of the cylinder

Surface area
2?r2 2?rh (where h height of cylinder and
the base of the lateral surface is the
circumference of circular base 2?r)
2?(5)2 2?(5)(12)
? 533.8
Surface area ? 534 square inches
C 2?r 2?(5)
5
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Surface Area

• Cone

Surface area
Circle base triangle
1 2
?r2 bh Where b perimeter of circle
(circumference) h slant height
Perimeter 2?r
Ex Ice cream cone
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Cone Example

• Find the area of the cone

10cm
Surface area
1 2
?r2 (2?r)h
5cm
25? 50?
75? ? 235.6
Surface area ? 236 cm2
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Homework

• Pg 464 -465
• 1-11