Math-How do I do this problem?

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An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep.

  • Math-Damon can you help me? -

    Do you know what kind of formula I could use to solve this?

  • Math-How do I do this problem? -

    sure
    change in volume = surface area * change in depth
    or
    dV = pi r^2 dh
    dV/dt = pi r^2 dh/dt = 12 ft^3/min
    so
    dh/dt = 6/(pi r^2)

    if r = 7, h = 24
    or
    r = (7/24)h = (7/24)(10) = 70/24
    so
    dh/dt = 6 / [ pi (70/24)^2 ]

  • Math-How do I do this problem? -

    Hmmm. I get
    r = 7/24 h
    so, dr = 7/24 dh
    r = 35/12 when h=10

    v = 1/3 pi r^2 h
    using the product rule,
    dv = 1/3 pi (2rh dr + r^2 dh)
    12 = pi/3 (2*(35/12)(10)(7/24 dh)+(35/12)^2 dh)
    12 = 1225/144 pi dh
    dh = 1728/1225 pi
    = 12^3/35^2 pi

    Maybe you can figure out whether one of us is correct.

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