Ellipsoid volume

From ancient times, people needed to measure the amount of various substances. Bulk substances and liquids could be measured by filling them with vessels of a certain capacity, determining their quantity by volume. The concept of volume in solid geometry is introduced similarly to the concept of area in plane geometry. In plane geometry, we determined the area like this: the area of ​​a polygon is the value of the part of the plane that the polygon occupies. To formulate the concept of volume similarly to this concept. The magnitude of the part of the space occupied by the geometric body is called the volume of this body. Volume is measured in "cubic" units.

Ellipsoid — is a surface in three-dimensional space obtained by the deformation of a sphere along three mutually perpendicular axes. The canonical equation of an ellipsoid in Cartesian coordinates, coinciding with the deformation axes of the ellipsoid: where are arbitrary positive numbers.

The volume of an ellipsoid is a number that characterizes the ellipsoid in units of volume. V = 4/3πabc