![]() For this ellipsoid, the difference between the equatorial radius and the polar radius (the semimajor and semiminor axes, respectively) is about 21 km (13 miles), and the flattening is about 1 part in 300. After using our calculator and reading this article, you’ll be confident about how to find the ellipsoid of an ellipsoid. In the text below, we will show you the volume calculator as well as to explain the ellipsoid volume formula. ![]() Often an ellipsoid of revolution (called the reference ellipsoid) is used to represent the Earth in geodetic calculations, because such calculations are simpler than those with more complicated mathematical models. This volume of an ellipsoid calculator will help you calculate the volume of an ellipsoid. See also Measuring the Earth, Modernized. As more accurate measurements became possible, further deviations from the elliptical shape were discovered. Isaac Newton predicted that because of the Earth’s rotation, its shape should be an ellipsoid rather than spherical, and careful measurements confirmed his prediction. In either case, intersections of the surface by planes parallel to the axis of revolution are ellipses, while intersections by planes perpendicular to that axis are circles. An oblate spheroid is formed by revolving an ellipse about its minor axis a prolate, about its major axis. If a and b are greater than c, the spheroid is oblate if less, the surface is a prolate spheroid. If two axes are equal, say a = b, and different from the third, c, then the ellipsoid is an ellipsoid of revolution, or spheroid (see the figure), the figure formed by revolving an ellipse about one of its axes. A special case arises when a = b = c: then the surface is a sphere, and the intersection with any plane passing through it is a circle. If a, b, and c are the principal semiaxes, the general equation of such an ellipsoid is x2/a2 + y2/b2 + z2/c2 = 1. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the centre. Quote from Britannica Ellipsoid, closed surface of which all plane cross sections are either ellipses or circles.
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