Q33 of 50 Page 1

150 spherical marbles, each of diameter 1.4 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 spherical marbles, d1 = 1.4 cm


⇒ r1 = d1/2 = 0.7 cm


Number of marbles = 150


Diameter of cylindrical vessel, d2 = 7 cm


⇒ r2 = d2/2 = 3.5 cm


Let the height of the water that rose when 150 marbles are dropped in the vessel = h


i.e. Volume of 150 marbles = volume of water that rose by height ‘h’ inside the vessel


We know that volume of sphere = (43) πr3 and volume of cylinder = πr2h



⇒ 50 (4) (0.7)3 = (3.5)2 h


⇒ 200 (0.343) = (12.25) h


⇒ 68.6/12.25 = h


⇒ h = 5.6


∴ The rise in the level of water in the vessel is 5.6 cm.


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