SOLUTION: Water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same time water is being pumped into the tank at a constant rate. The tank has a height of 6m and

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Question 143541: Water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same time water is being pumped into the tank at a constant rate. The tank has a height of 6m and a diameter of 10 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2m, find the rate at which the water is being pumped into the tank.
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
"The tank has a height of 6m and a diameter of 10 m" __ 6/10=H/(2r) __ 12r=10H __ r=(5/6)H

V=(1/3)(pi)(r^2)(H) __ substituting __ V=(1/3)(pi)[(5/6)H]^2(H) __ V=(25/108)(pi)(H^3)

differentiaitng __ dV=(25/108)(pi)(3)(H^2)(dH) __ dV=(25/36)(pi)(H^2)(dH)

let x="rate at which the water is being pumped into the tank" __ working in cm

x-10000=(25/36)(pi)(200^2)(20) __ x=1.76X10^6cm^3/min (approx)