Question

In a cylindrical vessel of diameter 24 cm, filled up with sufficient quantity of water, a solid spherical ball of radius 6 cm is completely immersed. Find the increase in height of water level.

Answer 1

Radius of spherical ball r = 6 cm, radius of cylindrical vessel r₁ = 12 cm

Since, the ball completely immersed into the vessel, the water level is increased.

Let the height of increased level.

Therefore,

The volume of increase water level = volume of ball

`pi xx (12)^2 xx x = 4/3 pi xx (6)^3`

`144 x = 4/3 xx 216`

`144x = 4 xx 72`

       `x = (4 xx 72)/144`

         x = 2 cm

Hence, the level of water increased by 2 cm.