If the ellipse $x^2+x^{2/9}=1$ in the xz-plane is revolved around the $z$-axis, to find the resulting ellipsoid surface we can replace $x$ by $\pm\sqrt{x^2+y^2}$. According to the book I'm using (Cracking the GRE), this gives us $x^2+y^2+\frac{1}{9}z^2=1$. My question is where does the $z$ come from?
2026-04-13 00:46:59.1776041219
Surface of revolution
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I think this is a mistake in the book. It should be $x^2 + \frac{1}{9} z^2 = 1$.