How to imagine or draw this geometry? And how to calculate its volume? Forevermore, can we calculate its surface area?
2026-05-15 19:06:33.1778871993
How to calculate the volume of $(\frac{x}{a}+\frac{y}{b})^2+(\frac{z}{c})^2 \le 1$ for a,b,c is the real number?
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After rotation of cylinder axis to make it parallel to coordinate axis it is found to be an infinite length elliptic cylinder. For prismatic/extruded sections we have
Volume
$$ =\pi p\,c L $$
where
$$ \dfrac{1}{p^2}=\dfrac{1}{a^2}+\dfrac{1}{b^2} $$
and cylinder length $ =L$ (not specifically given) and surface area likewise is ellipse perimeter $ 4 a E(e) $ in terms of complete elliptic integral of second kind multiplied by length $L$.