# A sphere of diameter 18 cm is dropped into a cylinder vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises byA. 3 cmB. 4 cmC. 5 cmD. 6 cm

Given: Diameter of a sphere: 18cm radius = = 9cm

Diameter of Cylindrical vessel: 36cm radius = = 18cm

It is given that Sphere is dropped into the cylindrical vessel containing some water.

Volume of sphere = Volume of water in Cylinder displaced (raised)

Let V1 be the volume of the Sphere

V1 = × π × (r1)3

V1 = × π × 93

Let V2 be the volume of the water displaced in the cylindrical vessel

V2 = π × (r2)2 × h (here r2 is the radius of the Cylinder and h is the level of water raised in the vessel after dropping the sphere into the cylindrical vessel)

V2 = π × 182 × h

Since V1=V2 × π × 93 = π × 182 × h

h = = = 3cm

The water level rises by 3cm when the dropped sphere is completely submerged in the cylindrical vessel.

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