\begin{array}{l}
V = {r^2}\pi H\\
H = \frac{V}{{{r^2}\pi }}\\
P = {r^2}\pi  + 2r\pi H\\
P = {r^2}\pi  + 2r\pi \frac{V}{{{r^2}\pi }}\\
P = {r^2}\pi  + 2V\frac{1}{r}\\
P' = 2r\pi  + 2V\left( { - \frac{1}{{{r^2}}}} \right)\\
P' = 2r\pi  - \frac{{2V}}{{{r^2}}}\\
P' = 0\\
2r\pi  - \frac{{2V}}{{{r^2}}} = 0/ \cdot \frac{{{r^2}}}{2}\\
{r^3}\pi  - V = 0\\
{r^3}\pi  = V\\
{r^3} = \frac{V}{\pi }\\
r = \sqrt[3]{{\frac{V}{\pi }}}
\end{array}