http://www.ck12.org Chapter 11. Surface Area and Volume
Example A
What is the surface area of the cone?
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 B
The surface area of a cone is 36πand the slant height is 5 units. What is the radius?
Plug in what you know into the formula for the surface area of a cone and solve forr.
36 π=πr^2 +πr( 5 ) Because every term hasπ,we can cancel it out.
36 =r^2 + 5 r Set one side equal to zero, and this becomes a factoring problem.
r^2 + 5 r− 36 = 0
(r− 4 )(r+ 9 ) = 0 The possible answers forrare 4 and− 9 .The radius must be positive,
so our answer is 4.Example C
Find the volume of the cone.