A sphere of diameter 5cm is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is 10cm. If the sphere is completely submerged, by how much will the level of water rise?

Solution:

Diameter of sphere = 5 cm

Radius of sphere, r = 5/2 = 5/2 cm

The diameter of the base of the vessel = 10 cm

Radius of the base of the vessel, R = 10/2 = 5 cm

Volume of sphere = (4/3)πr3

Volume of cylindrical vessel = πR2h

Volume of sphere = Volume of water raised in cylindrical vessel.

=> (4/3)πr3 = πR2h

=> (4/3)(5/2)3 = 52 h

=> h = (4/3)(5/2)3/52 = 5/6

The level of water rise = 5/6 cm.

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