Question

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

Options

• \[\frac{2}{9}\] cm

• \[\frac{4}{9}\]cm

• \[\frac{9}{4}\] cm

• \[\frac{9}{2}\]cm

Answer 1

The radius of sphere, r = 3 cm

The volume of sphere

\[= \frac{4}{3} \pi r^3 \]

\[ = \frac{4}{3}\pi \left( 3 \right)^3 \]

\[ = 36\pi {cm}^3\]

Since,

The sphere fully immersed into the vessel, the level of water be raised by x cm.

Then,

The volume of raised water = volume of sphere

`pi(4)^2 xx x = 36pi`

               `x = 36/16`

               `x = 9/4 cm`