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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 or cigar). If the minor axis is chosen, the surface is called an oblate spheroid (similar to the shape of the planet Earth).
A spheroid can also be characterised as an ellipsoid having two equal semi-axes, as represented by the equation
A prolate spheroid has one semiaxis longer than the other two, (a > b); an oblate spheroid has two equal semiaxes that are longer than the third one(a < b) and can resemble a disk.
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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.
Volume
Prolate spheroid:
- volume is
Oblate spheroid:
- volume is
where
- a is the semi-major axis length
- b is the semi-minor axis length
Surface area
A prolate spheroid has surface area
An oblate spheroid has surface area
 .
Here e is the eccentricity of the ellipse, defined as
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