2025 MSHS PRELIMS P2 Q9

The diagram shows a paper weight which is made up of a solid hemisphere of radius \(r\) cm, resting on top of a solid cylinder of radius \(2r\) cm and height \(h\) cm.

1. Given that the total volume of the solid is \(216\pi\text{ cm}^3\), express \(h\) in terms of \(r\).[2]
2. Show that the total surface area, \(A\text{ cm}^2\), of the solid is given by, \(A=\dfrac{25\pi r^2}{3}+\dfrac{216\pi}{r}\).[2]
3. Given that \(r\) can vary, find the value of \(r\) for which \(A\) has a stationary value. Find this value of \(A\) and determine whether it is a maximum or a minimum.[5]