Question

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

Answer 1

In two cylinders,

Ratio in radii of two cylinders $=2:3$
Ratio in their heights $=5:3$
Let $r_1$ and $r_2$ be the radii and $h_1,h_2$ be their heights respectively.
$\therefore r_1:r_2=2:3$ and $h_1:h_2=5:3$
$\therefore \frac{r_1}{r_2}=\frac{2}{3}$ and $\frac{h_1}{h_2}=\frac{5}{3}$

Since, Surface area of the first cylinder $=2\pi rh$ square units
$\Rightarrow$The ratio of surface area of the two cylinders
$=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}$

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

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

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

$=\frac{10}{9}$
Hence, the ratio in their surface areas $=10:9$