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## Homework Statement

So I keep coming across problems that suggest finding the Volume of an ellipsoid using the volume of a ball ie:

Find the volume enclosed by the ellipsoid:

(x/a)^2 + (y/b)^2 + (z/c)^2 = 1

by using the fact that the volume of the unit ball in R^3 is 4pi/3

## Homework Equations

## The Attempt at a Solution

I keep getting stuck on this one. It seems like it will be some change of variables in which abc will eventually just pop out front of the usual expression for the volume of a ball. I keep thinking that I should be able to use spherical coords and a substitution like u = x/a, v = y/b and w = z/c. But then you just get the normal unit ball integral. I feel like it might come out of the limits of the integral in terms of P. That is, the maximum length of p is a function of [itex]\phi[/itex] and [itex]\theta[/itex] in the ellipsoid case. But with the above substitution then P is 1. Or I keep thinking it might come out of dP, but that hasn't been clear either.

I also keep thinking of plugging in for p -> p = [itex]\sqrt{u

^{2}+ v

^{2}+ w

^{2}}[/itex] = [itex]\sqrt{(psin \phi cos \theta)

^{2}/a + (psin \phi sin \theta)

^{2}/b + (pcos \phi cos \theta)

^{2}/c}[/itex] but then the p

^{2}term would cancel out.

Anyway, I am just going in circles. Does anybody have any suggestions?