Question

a right circular cone of diameter r cm and height 12 cm rest on the base of a right circular cylinder of radius r cm .There bases are in the same plane and the cylinder is filled with water upto the height of 12 cm .If the cone is then removed,find the height to which water level will fall

Answer 1

Diameter  of base of cone = r cmRadius of base of cone = r/2 cmRadius of base of cylinder = r cmHeight of cone =12cmHeight of water in cylinder before cone was taken out = 12cm∴Volume of water left in cylinder when cone is removed out = Volume of water - Volume of cone= πr2h = (1/3)πr2h= 12πr2 – (1/3)π(r/2)2(12)= 12πr2 - πr2= 11πr2Thus, height to which the water level will fall = 11 cm, which is the present height of water left in cylinder.