Question

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

Answer 1

Answer:

$20\:\mathrm{in}$

Step-by-step 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 $\ell$:

$200\pi=10\pi\ell,\\\ell=\frac{200\pi}{100\pi}=\boxed{20\:\mathrm{in}}$

*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.