Differentiation - Problems Involving Maximisation and Minimisation

The diagram shows a paper weight which is made up of a solid hemisphere of radius, \(r\) cm, resting on the top surface of a solid cylinder of height \(h\) cm.

1. Given that the total volume of the solid is \(360\pi\) cm\(^3\), express \(h\) in terms of \(r\).
2. Show that the total surface area, \(A\) cm\(^2\), of the solid is given by \(A = \frac{720\pi}{r} + \frac{5}{3}\pi r^2\).
3. Find the minimum total surface area of the solid, leaving your answer in terms of \(\pi\). Show your working clearly.