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.

mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt

Pyramid Arena

mynameismr.info/.../Surface%20Area%20of%20Pyramids%20&%20Cones.ppt

Surface Area of a Cone

Unit 6, Day 4 Mr. Zampetti 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



r

 

r

2  

r B

 

r

2

r

Lateral Area of a Cone

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

r

2 L.A. =  

r

Example 1: • Find the surface area of the cone to the nearest whole number. a.

4 in.

6 in.

r = 4 slant height = 6

S

   

r

2 (4) 2    

r

(4)(6)     16 

40

 

in

2 24

40(3.14)



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

2  (12) 2 2

h

 169  (5) 2 13 Next, r = 12,

S

 

r

2  2  

r

13.

   (12) 144   300      156 (12)(13) 

ft

2

On your own #1

Calculate the surface area of:

S

 

r

2  

r

•S =  (7) 2 +  (7)(11.40) •S = 49  + 79.80

 •S = 128.8



On your own #2

Calculate the lateral area of:

S

 

r

2  

r

•L.A. =  (5)(13) •L.A. = 65 

Homework

Work Packet: Surface Area of Cones