A sphere of diameter 6cm 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?

Given

Diameter of sphere, d₁ = 6 cm

⇒ Radius of sphere, r₁ = 3 cm [∵ diameter = 2 × radius]

Diameter of cylindrical vessel, d₂ = 12 cm

⇒ Radius of cylindrical vessel, r₂ = 6 cm

Formulas

Volume of sphere

Volume of cylinder = πr²h

Where,

r = radius of sphere/base radius of cylinder

h = height of cylinder

Let the water rise be ‘h’ cm, then

Volume of water displaced = Volume of sphere

⇒ Volume of cylinder with height ‘h’ = Volume of sphere

Putting values, we get

⇒ 36h = 36

⇒ h = 1 cm