Question

Two circular cylinders of equal curved surface areas have their heights in the ratio $1:2$, then find the ratio of their radii.

Answer 1

Let $S_1$ and $S_2$ be the curved surface areas of the cylinders.

$\frac{S_1}{S_2}=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}$

Given:$S_1=S_2$

$\Rightarrow \frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}=1$

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

Given:$h_1:h_2=1:2$ or $\frac{h_1}{h_2}=\frac{1}{2}$

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

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

Hence,the ratio of their radii is $2:1$