Prolate Spheroid

A Spheroid which is pointy'' instead of squashed,'' i.e., one for which the polar radius is greater than the equatorial radius , so . A prolate spheroid has Cartesian equations

 (1)

The Ellipticity of the prolate spheroid is defined by
 (2)

so that
 (3)

Then
 (4)

The Surface Area and Volume are
 (5) (6)

See also Darwin-de Sitter Spheroid, Ellipsoid, Oblate Spheroid, Prolate Spheroidal Coordinates, Sphere, Spheroid

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 131, 1987.