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The Third Semi Axis of Ellipsoid is the length of the segment of third cartesian coordinate axis from the center of the Ellipsoid to its surface. It represents one of the three principal radii that define the size and shape of an ellipsoid.
The calculator uses the formula:
Where:
Explanation: This formula calculates the third semi axis when the volume and the other two semi axes are known, based on the volume formula for an ellipsoid.
Details: Calculating the third semi axis is essential for understanding the complete geometry of an ellipsoid, which has applications in physics, engineering, astronomy, and computer graphics where ellipsoidal shapes are used.
Tips: Enter the volume of the ellipsoid in cubic meters, and the lengths of the first and second semi axes in meters. All values must be positive numbers greater than zero.
Q1: What is an ellipsoid?
A: An ellipsoid is a three-dimensional geometric shape that is a deformation of a sphere, defined by three perpendicular axes of different lengths.
Q2: How is this different from a sphere?
A: A sphere has all three axes equal in length, while an ellipsoid has three different axes (or at least two different axes in the case of a spheroid).
Q3: What are some real-world applications of ellipsoids?
A: Ellipsoids are used in geodesy to model the Earth's shape, in physics for potential theory, in medicine for modeling organs, and in computer graphics for 3D modeling.
Q4: Can this formula be rearranged to find volume?
A: Yes, the volume formula for an ellipsoid is \( V = \frac{4}{3}\pi abc \), which can be rearranged to find any of the variables when the others are known.
Q5: What units should I use for the inputs?
A: The calculator expects consistent units (all in meters for lengths and cubic meters for volume). You can use any unit system as long as you maintain consistency.