150 spherical marbles, each of diameter 14 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

Given,


Diameter of marble = 1.4 cm


Radius of marble = 0.7 cm


Number of marbles = 150


Diameter of cylinder = 7cm


Radius of cylinder = 3.5cm


150 × Volume of spherical marbles = volume of cylindrical vessel
150 x × π × 0.7 × 0.7 × 0.7 = π × 3.5 × 3.5 × h


50 x 4 x (0. 7)3 = (3.5)2 x h


200 x 0.343 = 12.25 x h


= 5.6 = h


So,


h = 5.6 cm


The rise in the level of water in the vessel (h) = 5.6 cm


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