? 發問於 科學及數學數學 · 1 十年前

related rate

water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same time that water is being pumped into the tank at a constant rate.the tank has height 6m and the diameter at the tip is 4m. if the water level is rising at a rate 20cm/min when the height of the water is 2m.find the rate at which water is being pumped into the tank.

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  • 1 十年前
    最愛解答

    let x be rate at which water is being pumped into the tank

    let h, V be height and volume of the water at time t

    V

    = (1/3) pi (h/3)^2 h

    = pi h^3 / 27

    dV/dt = (pi h^2 / 9) dh/dt

    x - 10000 = (pi 200^2 / 9) (20)

    x = 800000 pi / 9 + 10000 = 289252.68 cm^3/min

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