150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some wate, 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
150×43×π×0.73=π×3.52×h
[Since,Volume of sphere=43πr3 and Volume of cylinder=πr2h]
50×4×0.73=3.52×h
200×0.343=12.25×h
h=68.612.25
h=5.6 cm
Height of water raised(h) = 5.6 cm