Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples

Find the surface area of a square pyramid with base edges 7.5 ft and slant height 12 ft.

The perimeter

p

of the square base is 4 X 7.5 ft, or 30 ft.

You are given = 12 ft and you found that

p

lateral area.

= 30, so you can find the L.A. =

p

2 Use the formula for lateral area of a pyramid.

= ( 30 )( 12 ) 2 = 180 Substitute.

Simplify.

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Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples (continued)

Find the area of the square base.

Because the base is a square with side length 7.5 ft,

B



s

2  7.5

2  56.25.

S.A. = L.A.



B

= 180  56.25

= 236.25

Use the formula for surface area of a pyramid.

Substitute.

Simplify.

The surface area of the square pyramid is 236.25 ft 2 .

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Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples

Find the lateral area of the hexagonal pyramid below. Round your answer to the nearest whole number.

Use the formula L.A. = 1 2

p

to find the lateral area of the pyramid.

The altitude of the pyramid, apothem of the base, and altitude of a lateral face form a right triangle, so you can use the Pythagorean Theorem to find the slant height .

= 20 2 + (4 3) 2 = 400 + 48 = 448

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Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples (continued)

L.A. = 1 2

p

= 1 2 ( 48 )( 448 ) Use the formula for lateral area.

Substitute.

Use a calculator.

The lateral area of the hexagonal pyramid is about 508 m 2 .

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Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples

Find the surface area of the cone in terms of .

S.A. = L.A.

+

B

=

r

+ = (5)(13) +

r

2 (5) 2 Use the formula for surface area of a cone.

Substitute the formulas for L.A. and

B

.

Substitute.

= 65 + 25 Simplify.

= 90 The surface area of the cone is 90 in.

2 .

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Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples

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. =

r

to find the lateral area of the cone.

The cone’s diameter is 1 ft, so its radius

r

is 0.5 ft.

The altitude of the cone, radius of the base, and slant height form a right triangle. Use the Pythagorean Theorem to find the slant height .

= 0.5

2  1.5

2 = 0.25  2.25 = 2.5

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Surface Areas of Pyramids and Cones LESSON 11-3 Additional Examples (continued)

Find the lateral area.

L.A. = = (

r

0.5

) 2.5

Use the formula for lateral area of a cone.

Substitute 0.5 for

r

and 2.5 for .

Use a calculator.

The lateral area of the cone is about 2.5 ft.

2

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