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Math Help - Calculus Word Problem

  1. #1
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    Calculus Word Problem

    Water is leaking out of an inverted conical tank at a rate of 7000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.
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  2. #2
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    Quote Originally Posted by kashifzaidi View Post
    Water is leaking out of an inverted conical tank at a rate of 7000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.

    \frac{r}{h} = \frac{2}{6}

    r = \frac{h}{3}

    V = \frac{\pi}{3}\left(\frac{h}{3}\right)^2 h

    V = \frac{\pi}{27} \cdot h^3

    \frac{dV}{dt} = \frac{\pi}{9} \cdot h^2 \cdot \frac{dh}{dt} = (volume rate in) - (volume rate leaking out)

    mind your units
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  3. #3
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    can u be more specific
    thanks
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  4. #4
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    Quote Originally Posted by kashifzaidi View Post
    can u be more specific
    thanks
    I think solving the problem short of substituting the given numerical values is specific enough.
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