9 A cylinder is to be cut out of the circular face of a solid hemisphere.
The cylinder and the hemisphere have the same axis of symmetry.
The cylinder has height \(h\) and the hemisphere has a radius of \(R\).
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9
- Show that the volume, \(V\), of the cylinder is given by
$$V = \pi R ^ { 2 } h - \pi h ^ { 3 }$$
9
- Find the maximum volume of the cylinder in terms of \(R\).
Fully justify your answer.