From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

Question

$\begin{array}{1 1} \frac{MR^2}{16 \sqrt 2 \pi} \\ \frac{4MR^2}{9 \sqrt 3 \pi} \\ \frac{4MR^2}{3 \sqrt 3 \pi} \\ \frac{MR^2}{32 \sqrt 2 \pi} \end{array} $