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Math Help - Help with work problem

  1. #1
    Member
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    Help with work problem

    The region R bounded by the y-axis, the lines y=4 and y=0, and the portion of the
    ellipse

    (x^2) +4(y-4)^2=100

    between the points (6,0) and (10,4) is revolved around the y-axis to form
    a container that is full of water. (See picture below.)

    ____________
    ...................'
    ................../
    ................./
    ...............-


    How do I set this up? Using the disk method?

    Thanks.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Yes - you each disc is centered on the y-axis, and you have the radius of each disc: R^2 = 100- 4(y-4)^2. The incremental volume of each disc is therefore:

    <br /> <br />
dV = \pi (100-4(y-4)^2) dy<br />

    Integrate this from y = 0 to y =4.
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