Question

Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their curved surface areas. 

Answer 1

Let the radii and height of two right circular cylinders be r₁, r₂ and h₁, h₂ respectively.

It is given that,

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

${\displaystyle \frac{\text{Curved surface area of cylinder 1}}{\text{Curved surface area of cylinder 2}}=\frac{2\pi r_1{h}_1}{2\pi r_2{h}_2}}$

= ${\displaystyle \left(\frac{r_1}{r_2}\right)\times \left(\frac{h_1}{h_2}\right)}$

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

= ${\displaystyle \frac{2}{5}}$

∴ Ratio between their curved surface areas is 2 : 5.