A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball). If the minor axis is chosen, the surface is called an oblate spheroid (similar to the shape of the planet Earth).

 Prolate spheroid.



 Oblate spheroid.

The sphere is a special case of the spheroid in which the generating ellipse is a circle.
A spheroid is a special case of an ellipsoid where two of the three major axes are equal.
Volume
Prolate spheroid:
 volume is
Oblate spheroid:
 volume is
where
 a is the major axis length
 b is the minor axis length
Surface area
A prolate spheroid has surface area
An oblate spheroid has surface area
 2πb(b + a·arcsin(e)/e).
Here e is the eccentricity of the ellipse, defined as
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