Question

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

___

Answer 1

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

So,

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

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

$\Rightarrow H=0.933333cm$

$1m={10}^{-6}\mu m$

$\therefore H=9333.33\mu m$