Question

Two cylinders of same volume have their heights in the ratio $1:3.$ Find the ratio of their radii.

• A. $\sqrt{3}:1$
• B. $\sqrt{2}:1$
• C. $\sqrt{5}:2$
• D. $2:\sqrt{5}$

Answer 1

The correct option is A $\sqrt{3}:1$

Given that $h_1:h_2=1:3$

Volume of cylinder is $=\pi r^{2}h$
We have, $\pi r_1^2{h}_1=\pi r_2^2{h}_2$
$\Rightarrow \frac{r_1^2}{r_2^2}=\frac{\pi h_2}{\pi h_1}=\frac{h_2}{h_1}=\frac{3}{1}$
$\Rightarrow \frac{r_1}{r_2}=\frac{\sqrt{3}}{1}$
$\Rightarrow r_1:r_2=\sqrt{3}:1$