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

A. $$\frac{2}{{\sqrt 3 }}{r^2}$$

B. $$\frac{4}{{\ 3 }}{r^2}$$

C. $$\frac{8}{{3\sqrt 3 }}{r^3}$$

D. $$\frac{1}{{3\sqrt 3 }}{r^3}$$

Answer: Option C

Solution(By Examveda Team)

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
$$\eqalign{ & \sqrt 3 a = 2r \cr & \Rightarrow a = \frac{2}{{\sqrt 3 }}r \cr} $$
Volume :
$$\eqalign{ & = {a^3} \cr & = {\left( {\frac{2}{{\sqrt 3 }}r} \right)^3} \cr & = \frac{8}{{3\sqrt 3 }}{r^3} \cr} $$