NUMBAT OER - Open Educational Resources

3.2 Sphere and ellipsoids

Shape Area Volume
Sphere
(any point on the surface is distance r from the centre)
4 πr2 4 πr3 /3
Ellipsoid
(distance between a point on the surface and the centre defined by the lengths of three axes)
4 π ((L+ M + N)/3)1/p
where, p = 1.6075
L= xpyp
M = xpzp
N = ypzp
(see note below)
4 πxyz /3

Note: the formula for the surface area of an ellipsoid is an approximation