Answer:
[tex]20\:\mathrm{in}[/tex]
Step-by-step explanation:
The lateral surface area of a cone is given by [tex]A=\pi r\ell[/tex], where [tex]r[/tex] is the radius of the base of the cone and [tex]\ell[/tex] is the cone's slant height.
Solving for [tex]\ell[/tex]:
[tex]200\pi=10\pi\ell,\\\ell=\frac{200\pi}{100\pi}=\boxed{20\:\mathrm{in}}[/tex]
*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.
