Question

Two circular cylinders of equal volume have their heights in the ration 1:2. Ration of their radii is

(a) 1 : $\sqrt{2}$ (b) $\sqrt{2}$ : 1

(c) 1 : 2 (d) 1 : 4

Answer 1

Let $r_1$ and $h_1$ be the radius and height of the first cylinder, then

Volume = $\pi r_1^2{h}_1$

Similarly $r_2$ and $h_2$ are the radius and height of the second cylinder

$\therefore Volume=\pi r^2{h}_2$ But their volumes are equal,

$\therefore \pi r_1^2{h}_1=\pi r_2^2{h}_2$

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

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

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

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

$\therefore$ Ration in radii = $\sqrt{2}$ : 1

Hence the correct answer is $\sqrt{2}$ : 1