The moment of inertia of a solid sphere of density $\rho$ and radius R about its diameter is

Moment of inertia of sphere about it diameter $I=\frac{2}{5}M{R}^2$$=\frac{2}{5}\left(\frac{4}{3}\pi R^3\rho \right)R^2$              

I =$\frac{8\pi }{15}{R}^5\rho$$=\frac{8\times 22}{15\times 7}{R}^5\rho =\frac{176}{105}{R}^5\rho$