Question

The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height is __________.

Answer 1

Let r be the radius of base and h be the height of both right circular cylinder and right circular cone.

∴ Volume of the cylinder, V₁ = $\mathrm{\pi }{r}^{2}h$

Volume of the cone, V₂ = $\frac{1}{3}\mathrm{\pi }{r}^{2}h$

Now,

$\frac{V_1}{V_2}=\frac{\mathrm{\pi }{r}^{2}h}{{\displaystyle \frac{1}{3}}\mathrm{\pi }{r}^{2}h}=3$

⇒ V₁ : V₂ = 3 : 1

Thus, the ratio of the volume of a right circular cylinder and a right circular cone of the same base and height is 3 : 1.

The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height is ___3 : 1___.