Equation of Ellipsoids
When two axes, such as m and n, are in equivalency and distinct from the third, o, the ellipsoid is referred to as a spheroid or an ellipsoid of revolution. An ellipse is rotated about one of its axes to generate an ellipsoid shape.
The spheroid will be oblate if m and n are more than o; if they are smaller, the surface will be prolate. Having stated that, a classic equation of such an ellipsoid is x²/m² + y²/n² + z²/o² = 1, assuming that m, n, and o are the primary semiaxes. When m = n = o, there is a special case where the surface is a sphere and the bisection through which any plane passes is a circle.
Volume of an Ellipsoid
Volume of an Ellipsoid Formula: An ellipsoid can be called a 3D equivalent of an ellipse. It can be derived from a sphere by contorting it using directional scaling or, more broadly, an interpolation conversion. An ellipsoid is evenly spaced at three coordinate axes that intersect at the center.
In this article, we will discuss the volume of an ellipsoid, and provide solved examples on it.
Table of Content
- What is an Ellipsoid?
- Equation of Ellipsoids
- Volume of Ellipsoid Formula
- Solved Examples on Volume of an Ellipsoid
- Volume of an Ellipsoid Practice Problems
The above picture shows an ellipsoid, its three semi-axes denoted a, b, and c are also shown. Ellipsoids occur in nature in the shape of watermelons, as well as the female reproductive organs and male urinary bladder. The study of the ellipsoid volume is necessary as it helps doctors calculate the volume of ovaries and urinary bladders.