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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.
Solution
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.
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