Question

If a cylinder and a cone are of the same radius and height, then how many cones full of milk can fill the cylinder?

Answer 1

Given that a cone and a cylinder are of same radius and height.

To find out: How many cones full of milk can fill the cylinder?

Let the same radius and height be $r$ and $h$ respectively for both the cone and the cylinder.

Also, let $x$ number of cones that fill the cylinder.

Hence, $x\times \text{(volume of cone) = volume of cylinder}$

We know that, volume of a cone $=\frac{1}{3}\times \pi r^{2}h$

and volume of a cylinder $=\pi r^{2}h$

$\therefore x\times \frac{1}{3}\pi r^{2}h=\pi r^{2}h$

$\Rightarrow x=3$

Hence, $3$ cones full of milk will fill the cylinder.