150 marbles each of diameter 1.4cm are dropped in a cylinderical vessel of diameter 7cm containing some water which are completely immersed in water. find the rise in the level of water in the vessel
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
Let the height of the water raised when 150 spheres are dropped in the vessel.
volume of 150 marbles = volume of water raised by height 'h' inside the vessel
150 * 4 / 3 * pie * 0.7 * 0.7 * 0.7 =pie * 3.5 * 3.5 *h [vol. of sphere = (4/3) pie r3 ; vol. of cylinder = pie r2 h]
50 * 4 * (0. 7)3 = (3.5)2 * h
200 * 0.343 = 12.25 * h
68.6 / 12.25 = h
5.6 = h
Height of water raised(h) = 5.6 cm