Question

If a cone has a surface area of 822.78cm^2 and a diameter of 18cm, find the slant height of the cone

Answer 1

Answer:

$20.11\ cm$

Step-by-step explanation:

we know that

The surface area of the cone is equal to

$SA=\pi r^{2}+\pi rl$

where

r is the radius

l is the slant height

In this problem we have

$SA=822.78\ cm^{2}$

$r=18/2=9\ cm$ -----> the radius is half the diameter

substitute and solve for l

$822.78=\pi (9)^{2}+\pi (9)l$

$822.78=81\pi +9\pi l$

$l=(822.78-81\pi)/9\pi$

$l=(822.78-81(3.14))/9(3.14)=20.11\ cm$