Question

150 spherical marbles, each of diameter 1.4cm, are dropped in the cylindrical vessel of diameter term containing some water, which are completely immerged in water. Find the rise in the level of water in vessel.

Answer 1

The diameter of the vessel is not given. The question is solved assuming the diameter to be 7cm
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
Volume of each marble = 4 3 × π × r3 = 4 3 × 22 7 × (0.7)3 = 1.44
Volume of 150 marbles = 1.44 × 150 = 216 cu cm
Let the rise in level of water in the cylindrical vessel = 'h' cm
Diameter of the vessel = 7 cm
Radius of the vessel = 3.5 cm
Volume of the increased level of the water = π × r2 × h = 22 7 × (3.5)2 × h
Volume of the increased level of the water = Volume of 150 marbles
22 7 × (3.5)2 × h = 216
⇒ h = 5.6 cm
Therefore, rise in level of water in the vessel is 5.6 cm