(i)[2]
Show that the cylinder height is $0.3\,\text{m}$.
(ii)[4]
The cylinder is now split into two equal parts, and the half not joined to the hemisphere is removed. The cut is made at right angles to the axis of symmetry, so the resulting object is a hemisphere plus a cylinder with half the original height. Find the distance of the centre of mass of the new object from $O$.
(iii)[3]
The new object is placed with its hemispherical end on a rough horizontal surface. It is kept in equilibrium by a force of magnitude $P\,\text{N}$ acting along its axis of symmetry, which makes an angle of $30^\circ$ with the horizontal. Find $P$.