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oblate spheroid |
oblate spheroid |
A spheroid is a quadric
surface obtained by rotating an ellipse about one of its
principal axes; in other words, an ellipsoid with two
equal semi-diameters.
If the ellipse is rotated about its major axis, the
result is a prolate (elongated) spheroid, like a rugby
ball. If the ellipse is rotated about its minor axis,
the result is an oblate (flattened) spheroid, like a
lentil. If the generating ellipse is a circle, the
result is a sphere.
Because of its rotation, the Earth's shape is more like
an oblate spheroid than a sphere. In cartography, in
fact, the Earth is often assumed to be a standard oblate
spheroid. In the current World Geodetic System model,
the radius is approximately 6,378.137 km at the equator
and 6,356.752 km at the poles (a difference of over 21
km).
Volume
The volume of a spheroid (of any kind) is

In experimental
biology, tumor growth is approximated to take the shape
of a spheroid. Often, cancer studies involve the
implantation of tumors subcutaneously in mice. Such
studies require a simple mechanism by which to evaluate
tumor burden. One such method is for two blinded
researchers to measure tumor dimensions length and width
with calipers. The depth is not measured. Tumor volume
in cubic millimeters can be approximated with the
following formula:
Volume =
0.52(Width^2)Length.
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