${\displaystyle \left({\frac {x}{a}}\right)^{2}+\left({\frac {y}{a}}\right)^{2}+\left({\frac {z}{b}}\right)^{2}\leq 1}$

${\displaystyle {\frac {4}{3}}\pi a^{2}b}$

${\displaystyle 2\pi \left(a^{2}+{\frac {b^{2}\tanh ^{-1}e}{e}}\right)\quad {\mbox{if }}a>b}$

${\displaystyle 2\pi \left(a^{2}+{\frac {ab\operatorname {Sin} ^{-1}e}{e}}\right)\quad {\mbox{if }}b>a}$

${\displaystyle e={\sqrt {1-\left({\frac {\beta }{\alpha }}\right)^{2}}}}$