at any water depth y, the radius of the water surface is r/y = 3.25/8 = .40625
So, r = .40625y
when the water has depth y, the volume of water
v = 1/2 pi r^2 y = 1/2 pi (.40625y)^2 y
= 0.259 y^3
so,
dv/dt = 0.777 y^2 dy/dt
when the water is 4.5m (using cm for all measurements),
dv/dt = .777 (450)^2 (29) = 4,562,932 cm^3/min
so, since the tank is losing 500,000 cm^3/min, the inflow rate is that much greater:
5,062,932 cm^3/min
Water is leaking out of an inverted conical tank at a rate of 500.000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8.000 meters and the diameter at the top is 6.500 meters. If the water level is rising at a rate of 29.0 centimeters per minute when the height of the water is 4.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
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