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A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. Three particular cases of a spheroid are:
If the ellipse is rotated about its major axis, the surface is a prolate spheroid (similar to the shape of a rugby ball).
If the ellipse is rotated about its minor axis, the surface is an oblate spheroid (similar to the shape of the planet Earth or a pancake).
If the generating ellipse is a circle, the surface is a sphere (completely symmetric).
Alternatively, a spheroid can also be characterised as an ellipsoid having two equal equatorial semi-axes (i.e., ax = ay = a), as represented by the equation
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Surface area
A prolate spheroid has surface area
ight)=2pileft( rac+b^2
ight).,!
An oblate spheroid has surface area
ight)
ight),,!
where
is the semi-major axis length;
is the semi-minor axis length;
ight)=2arctanleft(sqrt
ight)quadmathrm,,!
ight)=2arctanleft(sqrt
ight)quadmathrm;,!
(sin(oε) is frequently expressed as the eccentricity, "e")
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Volume
Prolate spheroid:
volume is
Oblate spheroid:
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See also
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