Warm up: Finding the Areaof a Lateral Face• Architecture. The lateral faces of the

Pyramid Arena in Memphis, Tennessee, are covered with steal panels. Use the diagram of the arena to find the area of each lateral face of this regular pyramid.

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Surface Area of a Cone

Unit 6, Day 4Mr. Zampetti

With slides from www.cohs.com/.../229_9.3%20Surface%20Area%20of%20Pyramids%20and%20Cones%20C...

Pyramids and Cones

• A cone has a circular base and a vertex that is not in the same plane as a base.

• In a right cone, the height meets the base at its center.

• The height of a cone is the perpendicular distance between the vertex and the base.

• The slant height of a cone is the distance between the vertex and a point on the base edge.

Height

Lateral Surface

The vertex is directly above the center of the circle.

Baser

Slant Height

r

Surface Area of a Cone• Surface Area = area of base + area of sector

= area of base + π(radius of base)(slant height)

S B r 2r r

2B r r

Lateral Area of a Cone

• Since Lateral Area = Surface Area – area of the base

2r r L.A. =

Example 1:• Find the surface area of the cone to the nearest

whole number. a. r = 4 slant height = 64 in.

6 in.

2S r r 2(4) (4)(6)

16 24 4040(3.14)

2126 .in

Example 2:• Find the surface area of the cone to the nearest

whole number.b.

First, find the slant height. Next, r = 12,

12 ft.

5 ft.

2 2 2r h 2 2(12) (5)

144 25 169 169 13

13.2S r r

2(12) (12)(13) 144 156 300

2942 .ft

On your own #1

Calculate the surface area of:

•S = (7)2 + (7)(11.40)

•S = 49 + 79.80

•S = 128.8

2S r r

On your own #2Calculate the lateral area of:

•L.A. = (5)(13)

•L.A. = 65

2S r r L.A. =

Homework

Work Packet:Surface Area of Cones