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Volume of an ellipsoid

  1. Apr 27, 2006 #1
    Well, I have a small problem. I know the general formula for the volume of an ellipsoid. But I have a task to find it with the help of an integral. Can you explain me how to do this?
     
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  3. Apr 27, 2006 #2

    Curious3141

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    Last edited: Apr 27, 2006
  4. Apr 27, 2006 #3
    Thank you very much, the information is great.
    And can you write the formula like in that post but for an ellipsoid where a, b and c are different.
     
  5. Apr 27, 2006 #4

    siddharth

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  6. Apr 27, 2006 #5

    Curious3141

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    No, that's for a spheroid (two axes equal). For the general ellipsoid use the triple integral method. Of course the final answer comes out to a simple [tex]V = \frac{4}{3}\pi abc[/tex], it's just the derivation that's involved.
     
    Last edited: Apr 27, 2006
  7. Apr 30, 2006 #6
    And can you please show me how we can receive this
    [tex]V = \frac{4}{3}\pi abc[/tex]
    from this
    [tex]2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx[/tex]

    And can we also use this method?
     
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