If the surface area of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is :

Solution(By Examveda Team)

Let their radii be R and r
Then,
$$\eqalign{ & \frac{{4\pi {R^2}}}{{4\pi {r^2}}} = \frac{4}{{25}} \cr & \Rightarrow {\left( {\frac{R}{r}} \right)^2} = {\left( {\frac{2}{5}} \right)^2} \cr & \Rightarrow \frac{R}{r} = \frac{2}{5} \cr} $$
∴ Ratio of volumes :
$$\eqalign{ & = \frac{{\frac{4}{3}\pi {R^3}}}{{\frac{4}{3}\pi {r^3}}} \cr & = {\left( {\frac{R}{r}} \right)^3} \cr & = {\left( {\frac{2}{5}} \right)^3} \cr & = \frac{8}{{125}} \cr & = 8:125 \cr} $$