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Water is leaking out of an inverted conical tank at a rate of 700.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 10.0 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 26.0 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.

  • math -

    Let the rate of the input source be x cm^3 per minute
    So the effective dV/dt = (x- 700) cm^3/min

    let the height of the water level be h cm
    let the radius of the water level be r cm
    h/r = 10/1.75
    10r = 1.75h
    r = .175 h

    V = (1/3)π r^2 h
    = (1/3)π(.030625h^2)(h)
    = .010208333πh^3
    dV/dt = .030625πh^2 dh/dt
    x - 700 = .030625π(4.5)^2 (26)
    x = 750.655 cm^3/min

    check my arithmetic.

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