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 by
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.