Question

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

Answer 1

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Answer 2

Answer:

height to which the water level will fall = 11 cm, which is the present height of water left in cylinder.  

Step-by-step explanation:

Diameter  of base of cone = r cm

Radius of base of cone = r/2 cm

Radius of base of cylinder = r cm

Height of cone =12cm

Height 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

=  11πr2

Thus, height to which the water level will fall = 11 cm, which is the present height of water left in cylinder.