Question

A sphere of diameter 18cm is dropped into a cylindrical vessel of diameter 36cm which is partly filled with water. if the sphere is completely submerged, then the water level rises by a) 3cm b) 4cm c) 5cm d) 6cm

Answer 1

Answer:

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.