Question

A conical vessel whose internal radius is $5$ cm and height $24$ cm is full of water. The water is emptied into a cylindrical vessel with internal radius $10$ cm. Find the height to which the water rises.

• A. $2$ cm
• B. $4$ cm
• C. $6$ cm
• D. $8$ cm

Answer 1

The correct option is A $2$ cm

Volume of water in the conical vessel will be equal to the volume of water in the cylindrical vessel.

Volume of a Cylinder of Radius "$R$" and height "$h$" $=\pi R^{2}h$

Volume of a cone $=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base of the cone and $h$ is the height.

Hence, $\frac{22}{7}\times 10\times 10\times h=\frac{1}{3}\times \frac{22}{7}\times 5^2\times 24$

$\Rightarrow h=2$ cm

Hence, height of water in the cylindrical vessel is $2$ cm.