Water is leaking out of an inverted conical tank at a rate of 9800 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 16 centimeters per minute when the height of the water is 5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute

Question

Water is leaking out of an inverted conical tank at a rate of 9800  cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 16 centimeters per minute when the height of the water is 5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute

anonymous · Answer

V' in = V' ( currently left ) + V' leak
      V = ( π /3) r² h
         = ( π /3)  ( 1.5/ 8)² h³
-> V' = ( 1.5/ 8)²  π         h² h'
 plug h = 5, h' = .16 m/min :  ...
@katleynn782 Now the rest is just calculating. Don't forget convert into cm³ !