Question

Pavan filled water in a cylindrical vessel of radius 7cm and height 14cm. Then he dropped a spherical ball of radius 0.7cm. Height should be increased if he doesn't want water to overflow when the spherical ball is dropped into it? Give answer in micrometre and correct up to 2 decimal places.

Answer 1

Water that will fall out will be equal to the volume of the spherical ball dropped into the vessel.

So,

$\Rightarrow$ $\frac{4}{3}$ $\pi$ $r^3$ = $\pi$ $R^2$ H

$\Rightarrow$ $\frac{4}{3}$ $\times$ $\frac{22}{7}$ $\times$ ${\left(0.7\right)}^3$ = $\frac{22}{7}$ $\times$ ${\left(7\right)}^2$ $\times$ H

$\Rightarrow$ H = 0.0093333 cm

$\Rightarrow$ H = 9333.33 micrometre