Question

A sphere of diameter $5cm$ is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is $10cm$. If the sphere is completely submerged, by how much will the level of water rise?

Answer 1

Volume of water raised in vessel $=$ Volume of sphere

$\Rightarrow \pi r^{2}h=\frac{4}{3}\pi R^3\Rightarrow {\left(5\right)}^2\times h=\frac{4}{3}\times {\left(\frac{5}{2}\right)}^3\Rightarrow h=\frac{4\times 5\times 5\times 5}{5\times 5\times 3\times 8}=\frac{5}{6}cm$

$\therefore$ Rise in water level $=\frac{5}{6}cm$