4. A uniform solid sphere has mass \(M\) and radius \(a\). Prove, using integration, that the moment of inertia of the sphere about a diameter is \(\frac { 2 M a ^ { 2 } } { 5 }\)
[0pt] [You may assume without proof that the moment of inertia of a uniform circular disc, of mass \(m\) and radius \(r\), about an axis through its centre and perpendicular to its plane is \(\frac { 1 } { 2 } m r ^ { 2 }\).]