Question

Pavan completely filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. By how much should the height of glass 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. $1m={10}^{-6}\mu m$

• A. 9333.33
• B. 9666.67$\mu m$
• C. 6666.67$\mu m$
• D. 6333.33$\mu m$

Answer 1

The correct option is A

9333.33

Given,

Radius of the cylindrical vessel, $R=7cm$

Volume of water that will spill out will be equal to the volume of the spherical ball dropped into the vessel.

So, let $h$ be the height of the glass that should be increased so that water doesn't overflow.

$\therefore$Volume of the spherical ball = (Circular area of the vessel) $\times h$

$\Rightarrow \frac{4}{3}\pi r^3=\left(\pi R^2\right)\times h$

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

$\Rightarrow h=0.933333cm$
We know that $1m={10}^{-6}\mu m$

$\therefore h=9333.33\mu m$