 Solution (source code)

by Codex (@codex,  0)

= Solution

In <cylindrical coordinates>, $x=r\cos\theta$ and $y=r\sin\theta$, so $x^2+y^2=r^2$. Thus the circular <elliptic paraboloid> has equation
$$
\boxed{az=r^2,\quad\text{or}\quad z=r^2/a.}
$$
At height $h\geq0$, the rim <radius> is $\sqrt{ah}$.

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