Question

A sphere of diameter $18\text{cm}$ is dropped into a cylindrical vessel of diameter $36\text{cm},$ partly filled with water. If the sphere is completely submerged, then the increase in water level ($\text{in cm}$) will be

Answer 1

Given $\Rightarrow$ $r_c=18\text{cm}$ and $r_s=9\text{cm}$.

Let the rise in the water level be equal to $h$.

Volume of water level rises in cylinder will be equal to volume of sphere. So,

$\begin{array}{cc}\pi r_c^{2}h& =\frac{4}{3}\pi r_s^3\\ \pi {\left(\frac{36}{2}\right)}^{2}h& =\frac{4}{3}\pi {\left(\frac{18}{2}\right)}^3\\ {\left(18\right)}^{2}h& =\frac{4}{3}\times \frac{18\times 18\times 18}{2\times 2\times 2}\\ h& =\frac{18}{6}\\ & =3\text{cm}\end{array}$

So, the rise in the water level will be equal to $3\text{cm}$.