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Homework Help: Volumes of Revolution - Ellipsoid

  1. Aug 28, 2009 #1
    1. The problem statement, all variables and given/known data
    An ellipse is rotated around the y-axis, find the volume of this solid.

    2. Relevant equations
    x^2 / a^2 + y^2 / b^2 = 1
    \pi\int_{a}^-a x^2 dy

    3. The attempt at a solution
    I'm having trouble solving this; I know that the upper and lower bounds of the curve occur on the y-axis so I think that the ellipse equation can be rearranged to form;
    x^2 / a^2 + 0 = 1
    Thats where the upper and lower bounds for the integral come from.
    However I know that the volume of an ellipsoid is V = 4/3*pi*a*b^2.
    I just can't seem to get it to work.

    Any help is appreciated :)
  2. jcsd
  3. Aug 28, 2009 #2


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    Homework Helper

    Shouldn't your limits be ±b ?

    [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \Rightarrow \frac{x^2}{a^2}=1-\frac{y^2}{b^2}[/tex]

    find x2 in terms of y2, then put that into π∫x2 dy from b to -b and calculate.
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