Question

Pavan filled water in a cylindrical vessel of radius $6cm$ and height $11cm$. Then he gently dropped a spherical ball of radius $3cm$ inside the cylindrical vessel. What should be the maximum level of water in the cylindrical vessel before the spherical ball is dropped so that it doesn't get overflowed?

• A. 9333.33
• B. $9cm$
• C. $10cm$
• D. $11cm$

Answer 1

The correct option is C

$10cm$

Let $H$ be the level of water that will rise when the spherical ball is dropped inside the vessel

So, volume of the water that will fall out $=\pi R^{2}H$ [$R=6cm$]

Volume of the spherical ball $=\frac{4}{3}\pi r^3$ [$r=3cm$]

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

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

$\Rightarrow \frac{4}{3}\times \frac{22}{7}\times 3^3=\frac{22}{7}\times 6^2\times H$

$\Rightarrow 36=36H$

$\Rightarrow H=1cm$

So, the maximum level of water inside the vessel should be $11-H=11-1=10cm$