Question

The volumes of two hemispheres are in the ratio of 8:27. Find the ratio of their radii.

• A. 2:3
• B. 3:2
• C. 1:3
• D. 4:3

Answer 1

The correct option is A 2:3

Let $V_1\&V_2$ be the volumes.
Given,

$\frac{V_1}{V_2}=\frac{8}{27}$

Volume of hemisphere is given by
V = $\frac{2}{3}\pi r^3$

The ratio will be given by

$\Rightarrow \frac{\frac{2}{3}\pi r^3}{\frac{2}{3}\pi R^3}=\frac{8}{27}$

$\frac{r^3}{R^3}=\frac{8}{27}$

$\Rightarrow \frac{r}{R}=\frac{2}{3}$