Third Semi Axis of Semi Ellipsoid Calculator

Formula Used:

\[ c = \frac{3V}{2\pi ab} \]

Volume of Semi Ellipsoid (V):

m³

Bisected Axis of Semi Ellipsoid (a):

Second Semi Axis of Semi Ellipsoid (b):

Third Semi Axis of Semi Ellipsoid (c):

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1. What is the Third Semi Axis of Semi Ellipsoid?

The Third Semi Axis of Semi Ellipsoid is the length of the segment of third cartesian coordinate axis from the center of the elliptical face of Semi Ellipsoid to its boundary edge. It represents one of the three principal dimensions that define the shape and size of a semi-ellipsoid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ c = \frac{3V}{2\pi ab} \]

Where:

\( c \) — Third Semi Axis of Semi Ellipsoid (m)
\( V \) — Volume of Semi Ellipsoid (m³)
\( a \) — Bisected Axis of Semi Ellipsoid (m)
\( b \) — Second Semi Axis of Semi Ellipsoid (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

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 a semi-ellipsoid.

3. Importance of Third Semi Axis Calculation

Details: Calculating the third semi axis is essential for understanding the complete geometry of a semi-ellipsoid. It's particularly important in engineering, architecture, and physics applications where precise dimensional calculations are required for structural analysis, volume optimization, and spatial planning.

4. Using the Calculator

Tips: Enter the volume in cubic meters, and both semi axes in meters. All values must be positive numbers greater than zero. The calculator will compute the third semi axis using the mathematical relationship between these parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is a semi-ellipsoid?
A: A semi-ellipsoid is half of an ellipsoid, typically created by bisecting an ellipsoid through one of its principal planes.

Q2: How is this different from a full ellipsoid calculation?
A: For a full ellipsoid, the volume formula is \( V = \frac{4}{3}\pi abc \), while for a semi-ellipsoid it's \( V = \frac{2}{3}\pi abc \), hence the different formula for calculating the third axis.

Q3: What are typical applications of semi-ellipsoids?
A: Semi-ellipsoids are commonly used in architectural domes, tank design, antenna reflectors, and various engineering structures where curved surfaces are required.

Q4: Are there any limitations to this calculation?
A: This calculation assumes a perfect semi-ellipsoidal shape and may not account for manufacturing tolerances, material properties, or other real-world factors that might affect the actual dimensions.

Q5: Can this formula be used for imperial units?
A: Yes, but all measurements must use consistent units (all in feet, all in inches, etc.), and the result will be in the same unit of length.