A right circular cone has height 9 cm and radius of the base 5 cm. It is inverted and water is poured into it. If at any instant the water level rises at the rate of (π/A) cm/sec. Where A is the area of the water surface at that instant, show that the vessel will be full in 75 seconds.
Let r be radius of cross section at height h.
h=9cm and r=5cm....given
⇒r5=h9⇒r=5h9
Given, dhdt=πA
⇒dhdt=ππr2
⇒dhdt=8125h2
⇒2581∫90h2dh=∫90h33dt
⇒2581×7293=t
⇒t=75 seconds.