## Thomas' Calculus 13th Edition

$c=3$
We have the ellipsoid: $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ Its volume is: $\frac{4abc\pi}{3}$ Thus: $\frac{4*1*2*c*\pi}{3}=8\pi$ Solving for $c$, we get: $c=3$