Question

Two circular cylinders of equal volumes have their heights in the ratio 1:2 Find the ratio of their radii.

Answer 1

Volumes of two cylinders are equal.

Ratio in their height $h_1:h_2$ = 1 : 2

$\therefore \frac{h_1}{h_2}=\frac{1}{2}$

Let $r_1$ and $r_2$ be the radii of two cylinder, then $\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_1}=1$

$\Rightarrow \frac{r_1^2}{r_2^2}\times \frac{h_1}{h_2}=1$

$\Rightarrow \frac{r_1^2}{r_2^2}\times \frac{1}{2}=1\Rightarrow \frac{r_1^2}{r_2^2}=\frac{1\times 2}{1}=\frac{2}{1}$

$\therefore \frac{r_1}{r_2}=\sqrt{\frac{2}{1}}=\frac{\sqrt{2}}{1}$

$\therefore$ Ratio between their radii = $\sqrt{2}$ : 1