Question: An empty conical water container is placed on its base and water is poured into it through the vertex. It takes 20 minutes for the water level to rise to 40% of the height of the cone. How long will it take for the water level to rise to 70% of the height of the cone?

A: 22.8 minutes
B: 24.8 minutes
C: 35 minutes
D: 40 minutes

Ans: B
Solution: When water level rise upto 40 %.
Vol of water =1/3 πR²H-1/3πr²h
h = H-H*40/100
   = 3/5H

 r = 3/5R ( from triangle law of geometry)
So vol of water poured in 20 min = 1/3 π[R²H-(3/5R)²(3/5H)]
                                                   = 1/3 π[98/125R²H]

Now to raise the water to 70 %
h1 = H-H*70/100
   = 3/10H
 r1 = 3/10R
Vol of water will be = 1/3 π[R²H-(3/10R)²(3/10H)]
                               = 1/3 π[973/1000R²H]

Required time =( 973/1000)*(20)/(98/125)
                    = 24.8 min Ans