Question

The height and the base radius of a Cone and Cylinder are equal to the radius of Sphere. Find the ratio of their volumes.

Answer 1

Let $h$ and $r$ be the height and radius of the cone respectively.

Given that the height and the base radius of a Cone and Cylinder are equal to the radius of the Sphere.

Therefore,

Radius of sylinder $=r$

Height of cylinder $=h$

Now,

Volume of cone $\left(V_1\right)=\frac{1}{3}\pi r^{2}h.....\left(1\right)$

Volume of cylinder $\left(V_2\right)=\pi r^{2}h.....\left(2\right)$

Dividing equation $\left(1\right)$ by $\left(2\right)$, we have

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

$\Rightarrow \frac{V_1}{V_2}=\frac{1}{3}$

Hence the ratio of the volume of cone to that of cylinder is $1:3$.