A conical vessel of radius 10 cm and height 18 cm is filled with water. If the water is poured in a cylindrical vessel of radius 5 cm, find the height of water in the cylindrical vessel.

Base radius of conical vessel = r₁ = 10 cm

Height of conical vessel = h₁ =18 cm

Base radius of cylindrical vessel = r₂ = 5 cm

Let h be the height of water in the cylindrical vessel

(note that we does not need to know the height of cylindrical vessel just assume that the height will be till the water level)

As the water is transferred from conical vessel to cylindrical vessel volume is unchanged

Volume of conical vessel = πr₁²h₁

Volume of cylindrical vessel = πr₂²h

⇒ πr₁²h₁ = πr₂²h

⇒ r₁²h₁ = 3r₂²h

Substituting values

⇒ 10² × 18 = 3 × 5² × h

⇒ 100 × 6 = 25× h

⇒ h = 4 × 6

⇒ h = 24 cm

Therefore, height of water in the cylindrical vessel is 24 cm