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Math Help - work:

  1. #1
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    work:

    A tank in the form of an inverted right circular cone is 8m across the top and 10m deep. If the tank is filled to a height of 9m with water, find the work done in pumping the water to the top of the tank:

    the radius is 4, the depth is 10
    so
    the coordinates of the line passes through
    (4,0) and (0,-10)
    Equation of the line is: (y-(-10)) = 5/2(x - 0)
    x = 2/5y + 4

    work is :

    d(W) = 9180\pi(\frac{2}{5}y + 4)^2ydy
    and multiplied by y is the change in length to the top of the cone right?

    is the math model correct?
    9180\pi \int_{-9}^{-1} (\frac{2}{5}y + 4)^2 ydy

    thank you so much
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  2. #2
    MHF Contributor
    Joined
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    A tank in the form of an inverted right circular cone is 8m across the top and 10m deep. If the tank is filled to a height of 9m with water, find the work done in pumping the water to the top of the tank:

    the radius is 4, the depth is 10
    so
    the coordinates of the line passes through <---This should be "the line passes through the coordinates"
    (4,0) and (0,-10)
    Equation of the line is: (y-(-10)) = 5/2(x - 0)
    x = 2/5y + 4

    work is :

    d(W) = 9180pi[(2/5)y + 4)^2ydy
    and multiplied by y is the change in length to the top of the cone right?


    I assume your 9180 is the density of water in metric,
    9180 newton/cu.m.
    Should that not be 9800 newton/cu.m. ?
    Or, using your numbers, 9810 N/cu.m.?

    "the coordinates of the line passes ..."
    That should be "the line passes through the coordinates"

    "(4,0) and (0,-10)"
    That means your (0,0) is the center of the circular top of the cone.

    "and multiplied by y is the change in length to the top of the cone right?"
    Should be:
    "and it is multiplied by (-y) because (-y) is the change in height to the top....."

    ---------------------------------------------

    is the math model correct?
    9180\pi \int_{-9}^{-1} (\frac{2}{5}y + 4)^2 ydy


    The y in the "y dy" should be negative. Because all y's below the (0,0) are negative.

    The boundaries for integration should be from y = -10 to y = -1.
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