Find the ratio of the volume of a cube to that of a sphere which will fit inside it.

Let the radius of the shere be $R$ and the edge of the cube be $a$.

As, the sphere is fit inside the cube.

So, diameter of the sphere = edge of the cube

$\Rightarrow 2 R=a \quad \ldots$ (i)

Now,

The ratio of the volume of the cube to that of the sphere $=\frac{\text { Volume of the cube }}{\text { Volume of the sphere }}$

$=\frac{a^{3}}{\left(\frac{4}{3} \pi R^{3}\right)}$

$=\frac{(2 R)^{3}}{\left(\frac{4}{3} \pi R^{3}\right)} \quad[$ Using $(\mathrm{i})]$

$=\frac{3 \times 8 R^{3}}{4 \pi R^{3}}$

$=\frac{6}{\pi}$

$=6: \pi$

So, the ratio of the volume of the cube to that of the sphere is $6: \pi$.