8 The volume of a solid circular cylinder of radius \(r \mathrm {~cm}\) is \(250 \pi \mathrm {~cm} ^ { 3 }\).
- Show that the total surface area, \(S \mathrm {~cm} ^ { 2 }\), of the cylinder is given by
$$S = 2 \pi r ^ { 2 } + \frac { 500 \pi } { r }$$
- Given that \(r\) can vary, find the stationary value of \(S\).
- Determine the nature of this stationary value.