Question

A cone has a surface area of 200 pi square inches. If the radius of the

cone is 10 inches, find the length of the slant height.

Answer 1

`20\:\mathrm{in}`

Explanation:

The lateral surface area of a cone is given by
`A=\pi r\ell`, where
`r` is the radius of the base of the cone and
`\ell` is the cone's slant height.

Solving for
`\ell`:

`200\pi=10\pi\ell,\\\ell=(200\pi)/(100\pi)=\boxed{20\:\mathrm{in}}`

*Note: It is implied that the surface area of 200 pi square inches is lateral surface area and not total surface area, because it is impossible to obtain a total surface area of 200 pi with a radius of 10 inches.