Question

The radius of a two cylinder are in ratio $2:3$ and its height are in the ratio $5:3$ find the ratio of there curved surface area?

Answer 1

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Let $r_1,h_1$ and $r_2,h_2$ be the radius and height of the two cylinders respectively.

Given:$\frac{r_1}{r_2}=\frac{2}{3}$ and $\frac{h_1}{h_2}=\frac{5}{3}$

Curved surface area of cylinder$=2\pi rh$

Ratio:$=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}$

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

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

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

$=\frac{10}{9}$

$\therefore$ Ratio of their curved surface areas$=10:9$

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