# Math Help - Surface area and inscribed cone

1. ## Surface area and inscribed cone

I am having trouble with this one.

A right circular cylinder is inscribed within a right circular cone with height 10in and radius of base 3 inches. Find:

A) The total surface area of the cylinder in terms of the radius of the cylinder.
Now I know the the equation of the surface area of cylinder is; $A=2\pi r^2+ 2\pi r h$

but I don't know how to make it in terms of the radius?

$\frac{h}{3-r}=\frac{10}{3}$ and solved for h, so h= $10-\frac{10r}{3}$ then just plugged in and got... $A(r)=20\pi r-\frac{14\pi r^2}{3}$