Question

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes 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.

It is given that,

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

Now,

$\frac{\mathrm{Volume}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{Volume}\mathrm{of}\mathrm{second}\mathrm{cylinder}}$

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

$={\left(\frac{r_1}{r_2}\right)}^2\times \frac{h_1}{h_2}$

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

$=\frac{4}{9}\times \frac{5}{3}$

$=\frac{20}{27}$

∴ Volume of first cylinder : Volume of second cylinder = 20 : 27

Thus, the ratio of volumes of two cylinders is 20 : 27.

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is ___20 : 27___.