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Question:

A conical vessel, with base radius 5cm and height 24cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10cm. Find the height to which the water will rise in the cylindrical vessel. (Use π=22/7)

Solution:

Given: Radius of a cone=r=5cm
Height of the cone=h=24cm
Radius of the cylinder=R=10cm
Height of the cylinder=H=?
Volume of water in conical vessel=Volume in cylindrical vessel
⇒1/3πr²h=πR²H
⇒1/3π5²(24)=π10²H
⇒200=100H
∴H=2cm.