12-6 Surface Area of Cones

Objectives

• Find lateral areas of cones.• Find surface areas of cones.

Cones

Slant Height

Right Cone

•The base is a circle and the vertex is point V

•The axis is the segment with endpoints that are the vertex and the center of the base.

•The segment that has the vertex as one endpoint and is ⊥ to the base is called the altitude of the cone.

l

V

r

Axis and Altitude

Axis

Altitude

Oblique Cone

V

l

X

Lateral Area of Cones

l

V

r

rl

Lateral Area of Cones

l

V

r

rl

Lateral Area= slant height x π x radius

or

L=πrl

Example 1

4cm

12cm

Find the lateral area of the cone.

Example 1

4cm

12cm

Find the lateral area of the cone.

1. L= πrl

2.L= π(4)(12)

3.L=150.8

Lateral area= 150.8cm2

Total Surface Area

l

V

r

Total Surface Area

l

V

r

T= πrl + πr2

Example 2

6 m

8 m

Find the surface area of the cone.

Example 2

6 m

8 m

Find the surface area of the cone.

10 m

1. T= πrl + πr2

2. Use Pythagorean theorem to find l.

3. T= π(6)(10) + π62

4. T= 301.6

Surface Area = 301.6 m2

Example 3Johnny has an ice cream cone that has

a lateral area of 28 in and a slant height of 6 In. Find the diameter of his ice cream cone.

Example 3Johnny has an ice cream cone that has

a lateral area of 28 in and a slant height of 6 In. Find the diameter of his ice cream cone.

1. L= πrl

2. 28= πr(6)

3. r ≈1.5

4. d ≈3

5. Diameter ≈ 3 inches

Assignment

Page 668#7-24, 30-32