Question

The radii of the bases of a cylinder and a cone are in the ratio 3 : 4. If their height are in the ratio 2 : 3, then their volumes are in the ratio ________.

Answer 1

Let r be the radius and h be the height of the cylinder & R be the radius and H be the height of the cone.

It is given that,

$\frac{r}{R}=\frac{3}{4}$ and $\frac{h}{H}=\frac{2}{3}$ .....(1)

Suppose V₁ be the volume of the cylinder and V₂ be the volume of the cone.

$\therefore \frac{V_1}{V_2}$

$=\frac{\mathrm{\pi }{r}^{2}h}{{\displaystyle \frac{1}{3}}\mathrm{\pi }{R}^{2}H}$

$=3\times {\left(\frac{r}{R}\right)}^2\times \frac{h}{H}$

$=3\times {\left(\frac{3}{4}\right)}^2\times \frac{2}{3}$ [Using (1)]

$=\frac{9}{8}$

∴ Volume of the cylinder, V₁ : Volume of the cone, V₂ = 9 : 8

Thus, the ratio of volume of cylinder to the volume of cone is 9 : 8.

The radii of the bases of a cylinder and a cone are in the ratio 3 : 4. If their height are in the ratio 2 : 3, then their volumes are in the ratio __9 : 8__.