Question

A cylindrical vessel of radius $4cm$ contains water. A solid sphere of radius $3cm$ is lowered into the water, until it is completely immersed. Find the rise in the water level ( in $cm$) in the vessel.

Answer 1

Increase in volume of cylinder $=$ volume of sphere

Let increase in volume of cylinder be $=\pi r^{2}h$, where $r$ is its radius and $h$ is its height.

So, $\pi r^{2}h=\frac{4}{3}\pi r^3$

$\Rightarrow 16\pi h=\frac{4}{3}\pi 3^3$ where radius of the cylinder$=4$cm and radius of the sphere$=3$cm

$\Rightarrow h=\frac{4}{3}\times \frac{27}{16}=\frac{36}{16}=\frac{9}{4}=2.25$cm

$\therefore$ water rises by $2.25$cm in the vessel.