How to Calculate the Volume of an Ellipsoid

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You can measure volume even if it's in the shape of a tear drop. A tear drop is an ellipsoid, similar to an elongated sphere: a three-dimensional oval. A sphere is a three-dimensional circle, with equal height, width and depth, where no one point on the surface is farther from the center than any other. In the ellipsoid, there's also height, width and depth, but the points on its surface all lie at different distances from the center along each axis: the ellipsoid is a three-dimensional oval.

Things You'll Need

  • Ruler
  • Navigational divider
  • String
  • Measure the three semi-axes of the shape --a semi-axis is the distance from a central point in a three-dimensional figure -- either directly with a ruler or other calibrated measuring device. Or you can indirectly measure the distance by other means, perhaps with navigational divider, or with a tightly stretched string. Its longest semi-axis is designated "a," while the two shorter semi-axes are "b" and "c."

  • Multiply "a" times "b" times "c." If, for example, "a" is 12 inches, "b" is 4 inches and "c" is 3 inches, then 12 x 4 x 3 = 144.

  • Multiply the result, 144, by the constant, Pi, or 3.1416. The result is 452.3904. Divide 4 by 3: the result is 1.3333. Multiply this by the previous result, 452.3904.

  • Express the volume, 603.721, in cubic inches, since the example is for volume and began with "inches." The formula for the volume of an ellipsoid is expressed as 4/3 pi (xyz), where "x," "y," and "z" are the three axes of the ellipsoid, its height width and depth.

Tips & Warnings

  • When the three axes of a figure that appears to be an ellipsoid turn out to have equal measurements, the figure is no longer an ellipsoid, but a sphere. If two measurements are equal, like a cigar, it's called an "oblate ellipsoid of revolution."

References

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