The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is :

Answer: Option C

Clearly, the diagonal of the largest possible cube will be equal to the diameter of the sphere
Let the edge of the cube be a
$$\begin{array}{rl}& \sqrt{3}a=2r\\ & \Rightarrow a=\frac{2}{\sqrt{3}}r\end{array}$$
Volume :
$$\begin{array}{rl}& =a^3\\ & ={\left(\frac{2}{\sqrt{3}}r\right)}^3\\ & =\frac{8}{3\sqrt{3}}{r}^3\end{array}$$