CK-12 Geometry - Second Edition

11.5 Volume of Pyramids and Cones Contents http://www.ck12.org

From this, we can see that the lateral face’s edge is 2πrand the sector of a circle with radiusl. We can find the area
of the sector by setting up a proportion.

Area o f circle

Area o f sector

=

Circum f erence

Arc length

πl^2

Area o f sector

=

2 πl

2 πr

=

l

r

Cross multiply:

l(Area o f sector) =πrl^2

Area o f sector=πrl

Surface Area of a Right Cone: The surface area of a right cone with slant heightland base radiusrisSA=
πr^2 +πrl.

Example 5:What is the surface area of the cone?

Solution:In order to find the surface area, we need to find the slant height. Recall from a pyramid, that the slant
height forms a right triangle with the height and the radius. Use the Pythagorean Theorem.

l^2 = 92 + 212

= 81 + 441

l=

√

522 ≈ 22. 85

The surface area would beSA=π 92 +π( 9 )( 22. 85 )≈ 900. 54 units^2.

Example 6:The surface area of a cone is 36πand the slant height is 5 units. What is the radius?

Solution:Plug in what you know into the formula for the surface area of a cone and solve forr.