1.8: Optimising the volume of a cylinder

A closed cylinder has base radius $r$, height $h$ and volume $V$. It is given that the total surface area of the cylinder is $600\pi$ and that $V$, $r$ and $h$ can vary. Show that $V = 300\pi r - \pi r^{3}$.

Find the stationary value of $V$ and determine its nature.