Question

Volume of two hemispheres are in the ratio 27:125. Find the ratio of their radii.

Answer 1

Let the radius of one of the hemisphere be 'R'
And radius of another hemisphere be 'r'
Volume of a hemisphere =$\frac{2}{3}\pi r^3$
Now, ratio of their volume $=\frac{2}{3}\pi R^3:\frac{2}{3}\pi r^3$
Or, $\frac{27}{125}=\frac{R^3}{r^3}$
Or, $\frac{27}{125}=(\frac{R}{r}{)}^3$
Or, ${}^3\sqrt{\frac{27}{125}}=\frac{R}{r}$
Or, $\frac{3}{5}=\frac{R}{r}$
Or, $R:r=3:5$