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Math Help - finding the volume of the resulting ring..

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    finding the volume of the resulting ring..

    here is a problem im not sure how to start...

    the region bounded by y = r ^2 minus x^2, y=0, and x=0 is revolved about the y-axis to form a paraboloid. a hole, centered along the x-axis of revolution, is drilled through this solid. the hole has a radius k, 0< k< r. find the volume of the resulting ring (a) by integrating with respect to x and (b) by integrating with respect to y.

    im not sure where to start on this one. maybe this parabola is facing down with a rel max at (0,r)? so i would take the volume of the parabola and subtract it from the volume of the ring? or would it create a sphere since it is being rotated? im a little confused on this one....any help would be appreciated. thanks in advance.
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  2. #2
    Member
    Joined
    Feb 2010
    Posts
    133

    volume

    Hello,

    Basically you need to apply the correct formula provided and find the "bigger" voule and then the "smaller" volume". The difference between these will be the volume of the space between the two.
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