Ellipsoid is a sphere-like surface for which all cross-sections are ellipses.
Equation of standard ellipsoid body in xyz coordinate system is
where a - radius along x axis, b - radius along y axis, c - radius along z axis.
The volume of an ellipsoid is given by the following formula:
The surface area of a general ellipsoid cannot be expressed exactly by an elementary function. Knud Thomsen from Denmark proposed the following approximate formula:
, where p=1.6075