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## Main Question or Discussion Point

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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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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Curious3141

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We've covered this before. https://www.physicsforums.com/showthread.php?t=110799&highlight=volume+ellipsoid

And for the more special and simple case of a spheroid : https://www.physicsforums.com/showthread.php?t=76495&highlight=revolution

And for the more special and simple case of a spheroid : https://www.physicsforums.com/showthread.php?t=76495&highlight=revolution

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Thank you very much, the information is great.

And can you write the formula like in https://www.physicsforums.com/showpost.php?p=577097&postcount=12" but for an ellipsoid where a, b and c are different.

And can you write the formula like in https://www.physicsforums.com/showpost.php?p=577097&postcount=12" but for an ellipsoid where a, b and c are different.

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siddharth

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As Curious3141 already posted, in the link below, HallsofIvy explains it very well. What part do you not understand?

https://www.physicsforums.com/showthread.php?t=110799&highlight=volume+ellipsoid"

https://www.physicsforums.com/showthread.php?t=110799&highlight=volume+ellipsoid"

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- #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.-=nobody=- said:Thank you very much, the information is great.

And can you write the formula like in https://www.physicsforums.com/showpost.php?p=577097&postcount=12" but for an ellipsoid where a, b and c are different.

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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 http://libraryofmath.com/math/Calculus_III/directory/Example_Calculus_III_Volume_of_an_Ellipsoid.html" method?

[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 http://libraryofmath.com/math/Calculus_III/directory/Example_Calculus_III_Volume_of_an_Ellipsoid.html" method?

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