Transcript Surface Area of a Cone 5/8/07

Warm up: Finding the Area
of 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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Pyramid Arena
mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt
mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt
Surface Area of a Cone
Unit 5, Lesson 5
Mrs. King
With slides from
www.cohs.com/.../229_9.3%20Surface%20Area%20of%20Pyramids%2
0and%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.
Height
The vertex is directly
above the center of
the circle.
Lateral Surface
Slant Height
r
Base
r
• 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.
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  r r
2
B  r
2
r
Lateral Area of a Cone
• Since Lateral Area = Surface Area – area of the
base
= r
  rL.A. 
2
Example 1:
• Find the surface area of the cone to the nearest
whole number.
a.
r = 4 slant height = 6
4 in.
S  r r
2
  (4)   (4)(6)
2
6 in.
 16  24
 40
 40(3.14)
 126in.
2
Example 2:
• Find the surface area of the cone to the nearest
whole number.
b.
5 ft.
12 ft.
First, find the slant height.
2
r h
2
2
 (12)  (5)
2
2
 144  25  169
 169  13
 13.
Next, r = 12,
S   r 2  r
2
  (12)   (12)(13)
 144  156
 300
 942 ft.
2
On your own #1
Calculate the surface
area of:
S   r2   r
•S = (7)2 + (7)(11.40)
•S = 49 + 79.80
•S = 128.8
On your own #2
Calculate the lateral area of:
S  L.A.
r 2 =  r
•L.A. = (5)(13)
•L.A. = 65