A solid circular cylinder has a base radius of \(r\) cm and a height of \(h\) cm. The cylinder has a volume of \(1200\pi\text{ cm}^3\) and a total surface area of \(S\text{ cm}^2\).

(i) Show that

\(S=2\pi r^2+\frac{2400\pi}{r}.\)

(ii) Given that \(h\) and \(r\) can vary, find the stationary value of \(S\) and determine its nature.