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I thought spherical coordinates would be appropriate here, but I can't seem to find a correct answer.

b]1. Homework Statement [/b]

FInd the volume of the ellipsoid [tex]x^2 + y^2 + 4 z^2 = 100[/tex]

## Homework Equations

## The Attempt at a Solution

if I convert to spherical coordinates, I can reduce the following:

[tex] \rho^2sin^2\phi cos^2\theta + \rho^2sin^2\phi sin^2\theta + 4\rho^2cos^2\phi = 100 [/tex]

to

[tex] \rho=\sqrt{20} [/tex]

So I'm trying to set up my equation and get:

[tex]

\int_{0}^{2\pi}\int_{0}^{???}\int_{0}^{\sqrt{20}} d\rho d\phi d\theta

[/tex]

I'm fairly certain I'm not really on the right track, if someone could confirm that...

How do I find the value of [tex]\phi[/tex]?

And I'm not even really sure how to find the equation, although I'm guessing I am just being dense.

Any help would be appreciated.