# Find the volume of the ellipsoid

Find the volume of the ellipsoid x^2 + y^2 + 10z^2 = 16
solve for z... z=sqrt((16-x^2-y^2)/(10))
z = sqrt((16-r^2)/10)
so to find the volume, my integral looks like this:

latex doesnt seem to be working, so this could look messy...

2*int (from 0-2pi)*int(from 0-1)* sqrt((16-r^2)/(10))*r*dr*d(theta)

the 2 in front of the integral is to find the volume, since the integral only gives half of the volume right? is my setup correct? cause i keep getting the wrong answers

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Tide
Homework Helper
Your setup looks okay. I would have set it up this way:

$$V = 4\pi \int_{0}^{4\sqrt{5}/5} \int_{0}^{\sqrt {16-10z^2}} r dr dz$$

benorin
Homework Helper
Gold Member
The volume of the ellipsoid $$\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}+\left(\frac{z}{c}\right)^{2}=1$$ is $$V=\frac{4\pi}{3}abc$$.

Tide
The volume of the ellipsoid $$\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}+\left(\frac{z}{c}\right)^{2}=1$$ is $$V=\frac{4\pi}{3}abc$$.
I think the point was learning how to do volume integrals! Just a guess. 