Question

The volume 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 the volume of two hemispheres be $V_1$ and $V_2$ respectively.
We know that, volume of hemisphere = $\frac{2}{3}\pi r^3$

$\frac{V_1}{V_2}=\frac{\frac{2}{3}\pi r^3}{\frac{2}{3}\pi R^3}=\frac{8}{27}$
$\Rightarrow \frac{r^3}{R^3}=\frac{8}{27}$
$\Rightarrow \frac{r}{R}=\frac{2}{3}$