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

`20.11\ cm`

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`