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-=nobody=-
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Well, I have a small problem. I know the general formula for the volume of an ellipsoid. But I have a task to find it with the help of an integral. Can you explain me how to do this?
-=nobody=- said:Thank you very much, the information is great.
And can you write the formula like in https://www.physicsforums.com/showpost.php?p=577097&postcount=12" but for an ellipsoid where a, b and c are different.
An ellipsoid is a three-dimensional geometric shape that resembles an elongated sphere. It is defined as a surface that is obtained by rotating an ellipse about one of its axes.
The formula for calculating the volume of an ellipsoid is V = (4/3)πabc, where a, b, and c are the three semi-axes of the ellipsoid. Alternatively, it can also be calculated using the formula V = (4/3)πr1r2r3, where r1, r2, and r3 are the three radii of the ellipsoid.
The units for the volume of an ellipsoid depend on the units used for its semi-axes or radii. For example, if the semi-axes are measured in meters, the volume will be in cubic meters (m3).
No, the volume of an ellipsoid cannot be negative. It is a measure of the amount of space occupied by the ellipsoid and therefore must be a positive value.
The volume of an ellipsoid is generally larger than that of a sphere with the same semi-axes or radii. The difference in volume between an ellipsoid and a sphere increases as the eccentricity (deviation from a perfect sphere) of the ellipsoid increases.