Question

The radii of two right circular cylinders are in the ratio $2:3$ and the ratio of their curved surface areas is $5:6$. Find the ratio of their heights.

Answer 1

Let, Curved surface area of two right circular cylinders be $C_1$ and $C_2$ respectively.

Let, radii of two right circular cylinders be $r_1$ and $r_2$ respectively.

and height of two right circular cylinders be $h_1$ and $h_2$ respectively.

A.T.Q,

$\frac{C_1}{C_2}=\frac{5}{6}$

$⟹\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}=\frac{5}{6}$

$⟹\frac{2}{3}\times \frac{h_1}{h_2}=\frac{5}{6}[\because \frac{r_1}{r_2}=\frac{2}{3}]$

$⟹\frac{h_1}{h_2}=\frac{15}{12}=\frac{5}{4}$

$\therefore$ ratio of their heights $=5:4$