Question

A sphere with diameter $6cm$ is put into the water-filled in a cylindrical vessel with diameter $12cm$. How much the water level in the vessel will rise?

Answer 1

Given,Diameter of sphere $=6cm$ radius $\left(r\right)=\frac{6}{2}=3cm$
Volume of sphere $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times (3{)}^3$
Diameter of cylindrical vessel = $12cm$ radius $\left(R\right)=\frac{12}{2}=6cm$
When the sphere is put into the vessel, the water level rises by $h$.
$\therefore$ Volume of sphere = volume of water rise into the cylinder.
$\begin{array}{c}\frac{4}{3}\pi r^3=\pi R^{2}h\\ \frac{4}{3}\times 3\times 3\times 3=6\times 6\times h\end{array}$
$\begin{array}{cc}h& =\frac{4\times 3\times 3\times 3}{3\times 6\times 6}=\frac{108}{108}\\ & =1cm\end{array}$
Hence water level will rise in vessel=1cm