5 The region bounded by the \(x\)-axis, the line \(x = 8\) and the curve \(y = x ^ { \frac { 1 } { 3 } }\) for \(0 \leqslant x \leqslant 8\), is rotated through \(2 \pi\) radians about the \(x\)-axis to form a uniform solid of revolution. The unit of length is the metre, and the density of the solid is \(350 \mathrm {~kg} \mathrm {~m} ^ { - 3 }\).

1. Show that the mass of the solid is \(6720 \pi \mathrm {~kg}\).
2. Find the \(x\)-coordinate of the centre of mass of the solid.
3. Find the moment of inertia of the solid about the \(x\)-axis.