A conical vessel whose internal radius is 10 cm and height 18 cm is full of water. The water is emptied into a cylindrical vessel of internal radius 5 cm. Find the height to which the water rises.

Radius of base of conical vessel = r = 10 cm

Height of conical vessel = h = 18 cm

Volume of water in conical vessel = volume of cone

Volume of cone = πr²h

⇒ Volume of water in conical vessel = × π × 10² × 18

= π × 100 × 6

= 600π

Now this volume of water is transferred in cylindrical vessel whose radius is 5 cm

Let h₁ be the height up to which the water rises in the cylindrical vessel

Volume of water in cylindrical vessel = π(radius)²h

= π × 5² × h

= 25hπ

As water is transferred from conical vessel to cylindrical vessel volume of water is same

⇒ Volume of water in conical vessel = Volume of water in cylindrical vessel

⇒ 600π = 25hπ

⇒ 25h = 600

⇒ h =

⇒ h = 24 cm

Therefore, the height to which the water rises is 24 cm