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Volumes of Revolution - Ellipsoid

  • Thread starter Noir
  • Start date
  • #1
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Homework Statement


An ellipse is rotated around the y-axis, find the volume of this solid.


Homework Equations


x^2 / a^2 + y^2 / b^2 = 1
[tex]
\pi\int_{a}^-a x^2 dy
[/tex]


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 :)
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
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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