Question

Pavan 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 be increased if he doesn't want water to overflow when the spherical ball is dropped into it?

• A. 0.00934 cm
• B. 0.0834 cm
• C. 0.7084 cm
• D. 0.894 cm

Answer 1

The correct option is A 0.00934 cm

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

So,

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

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

$\Rightarrow H=0.00933333cm$

$\Rightarrow H=0.00934cm$

$\therefore 0.00934cm$ of height should be increased.