Oblate Spheroid - volume

vCalc Reviewed
Equation / Last modified by KurtHeckman on 2019/04/14 01:33
vCalc.Oblate Spheroid - volume

The Volume of an Oblate Spheroid equation (v = 4/3  π•b²•c) computes the volume of an oblate spheroid based on the semi-major(b) and semi- minor (c) axis with the assumption that the spheroid is generated via rotation around the minor axis (see diagram).  Ellipsoid_OblateSpheroid.png

INSTRUCTIONS: Choose units and enter the following:

  • (b) - semi-major axis, the distance from the oblate spheroid's center along the longest axis of the spheroid
  • (c) - semi-minor axis, the distance from the oblate spheroid's center along the shortest axis of the spheroid

Oblate Spheroid Volume (V): The volume is returned in cubic meters.  However, this can be automatically converted to other volume units (e.g. cubic yards, liters) via the pull-down menu.  

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The Math / Science

The formula for the volume of an oblate spheroid is:

              v = 4/3 π•b²•c


The oblate spheroid is an ellipsoid that can be formed by rotating an ellipse about its minor axis.  The rotational axis thus formed will appear to be the oblate spheroid's polar axis. The oblate spheroid is fully described then by its semi-major and semi-minor axes.

One important shape in nature that is close to (though not exactly) an oblate spheroid is the Earth which has a semi-minor axis (c) which is the polar radius of 6,356 kilometers, and a semi-major axis (b) which is the equatorial radius of 6,378 kilometers.  Consideration: what force would make the equatorial radius larger than the polar radius?

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