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).
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- Prolate spheroid.
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- Oblate spheroid.
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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
Last updated: 02-08-2005 12:31:52
Last updated: 05-03-2005 17:50:55