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Question

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?


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Solution

Diameter of sphere=5cm

Radius of sphere,,r=52cm

The diameter of the base of the vessel=10cm

Radius of the base of the vessel,R=102=5cm

Volume of sphere =43πr3

Volume of cylindrical vessel=πR2h

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

43πr3=πR2h43×(52)3=52hh=(43)(52)352=56

The level of water rise =56cm


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