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