# Volume of an ellipsoid

1. Apr 27, 2006

### -=nobody=-

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?

2. Apr 27, 2006

### Curious3141

Last edited: Apr 27, 2006
3. Apr 27, 2006

### -=nobody=-

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.

4. Apr 27, 2006

### siddharth

5. Apr 27, 2006

### Curious3141

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 $$V = \frac{4}{3}\pi abc$$, it's just the derivation that's involved.

Last edited: Apr 27, 2006
6. Apr 30, 2006

### -=nobody=-

$$V = \frac{4}{3}\pi abc$$
$$2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx$$