1. Problem

A closed cylinder has a total surface area equal to $600\pi$. Show that the volume, $V cm^3$, of this cylinder is given by the formula $V = 300\pi r - \pi r^3$, where $r cm$ is the radius of the cylinder.

I only managed to get $V = 300\pi r$. Where have I gone wrong?

2. $2 \pi r^2 + 2 \pi rh = 600 \pi$
$r^2 + rh = 300$
$V = \pi r^{2} h$
$\pi r(r^2 + rh) = 300 \pi r$
$\pi r^{2}h = 300 \pi r - \pi r^3$