The ratio of the volume of a cube to that of a sphere which will fit inside the cube is :

Answer: Option C

Let the edge of the cube be a
Then, volume of the cube = a³
Radius of the sphere $$=\left(\frac{a}{2}\right)$$
Volume of the sphere :
$$\begin{array}{rl}& =\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^3\\ & =\frac{\pi a^3}{6}\end{array}$$
∴ Required ratio :
$$\begin{array}{rl}& =a^3:\frac{\pi a^3}{6}\\ & =6:\pi \end{array}$$