Question

The radii of two cylinders are in the ratio $3:2$ and their heights are in the ratio $4:5.$ Calculate the ratio of their curved surface areas.

Answer 1

Let $r_1$ and $r_2$ be the radii of the cylinders respectively.

$\Rightarrow \frac{r_1}{r_2}=\frac{3}{2}$

Let $h_1$ and $h_2$ be the heights of the cylinders respectively.

$\Rightarrow \frac{h_1}{h_2}=\frac{4}{5}$

Ratio of Curved surface areas$=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}$

$=\frac{r_1{h}_1}{r_2{h}_2}$

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

$=\frac{3}{2}\times \frac{4}{5}$

$=\frac{12}{10}=\frac{6}{5}$

Hence,ratio of their curved surface areas is $6:5$