If the surface areas of two spheres are in the ratio of 4: 25, then the ratio of their volumes is · ABC26GN5004

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