A sphere has a radius of 8 cm and a cone has a radius of 4 cm. The height of the cone is 8 cm. Then find the ratio of the volume of the sphere to that of the cone.

Given, Radius of the sphere, r = 8 cm

Then, The volume of the sphere = $\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }\times 8^3=\frac{2048\mathrm{\pi }}{3} {\mathrm{cm}}^3$

Given, Radius of cone =  4 cm, Height of cone = 8 cm

The volume of the Cone = $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\mathrm{\pi }\times 4^2\times 8=\frac{128\mathrm{\pi }}{3} {\mathrm{cm}}^3$

Hence, the Required ratio = $\frac{{\displaystyle \frac{2048\mathrm{\pi }}{3}}}{{\displaystyle \frac{128\mathrm{\pi }}{3}}}=\frac{16}{1} = 16 :1$