A sphere of diameter 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is completely submerged in water, find by how much the surface level of water will be raised.
Diameter of sphere = 6 cm
Radius of sphere = r = 3 cm
Radius of cylinder = R = 6 cm
Let height of water raised be h cm.
Then, volume of water thus raised = R2h
Volume of water raised = volume of sphere
R2h = r3
R2h = r3
36h = 27
h = 1 cm
Therefore, water will be raised by 1 cm.
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