Question

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm partly filled with water. If the sphere is completely submerged

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.