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 micrometers and correct up to two decimal places.

___ $\mu m$

Answer 1

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

So,

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

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

$\Rightarrow H=0.933333cm$
$\because 1m={10}^{-6}\mu m$

$\therefore H=9333.33\mu m$