Q11 of 67 Page 195

A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

Diameter of sphere = 6 cm


Radius of sphere = rs = = 3 cm


The diameter of cylindrical vessel = 12 cm


Radius of cylindrical vessel = rc = = 6 cm


The volume of sphere submerged in water is equal to the volume of water rise


Let h be the rise of water level


it is given that the sphere is submerged completely


thus, volume of sphere = volume of water rise


volume of sphere = πrs3


volume of cylinder = πrc2h


⇒ πrs3 = πrc2h


⇒ 4rs3 = 3rc2h


⇒ 4 × 33 = 3 × 62 × h


⇒ 4 × 9 × 3 = 3 × 36 × h


⇒ 4 × 3 = 3 × 4 × h


⇒ 3 = 3 × h


⇒ h = 1 cm


Therefore, rise in water level in the cylindrical vessel is 1 cm


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