(i)[4]
Calculate the distance of the solid's centre of mass from $O$. [For a hemisphere of radius $r$, the volume is $\frac{2}{3}\pi r^3$.]
(ii)[4]
A cylindrical hole, of length $0.48\text{ m}$, beginning at the plane face of the solid, is cut along the axis of symmetry (see diagram). The centre of mass of the solid that remains is at $O$. Show that the cross-sectional area of the hole is $\frac{3}{16}\pi\text{ m}^2$.
(iii)[1]
The cylindrical hole can be made longer so that the solid still has its centre of mass at $O$. State the increase in the hole’s length.