Question

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

Answer 1

Let r₁ be the radius and h₁ be the height of first cylinder & r₂ be the radius and h₂ be the height of second cylinder.

$\therefore \frac{r_1}{r_2}=\frac{2}{3}$ and $\frac{h_1}{h_2}=\frac{5}{3}$ .....(1) (Given)

Now,

$\frac{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{second}\mathrm{cylinder}}$

$=\frac{2\mathrm{\pi }{r}_1{h}_1}{2\mathrm{\pi }{r}_2{h}_2}$

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

$=\frac{2}{3}\times \frac{5}{3}$ [Using (1)]

$=\frac{10}{9}$

∴ Curved surface area of first cylinder : Curved surface area of second cylinder = 10 : 9

Thus, the ratio of the curved surface areas of the two cylinders is 10 : 9.

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their curved surface areas is ___10 : 9___.