Total Surface Area Of Semi Ellipsoid Given Bisected Axis Calculator

Formula Used:

\[ TSA = \left(2\pi\left(\frac{\left(a\left(\frac{3V}{2\pi a c}\right)\right)^{1.6075} + \left(\left(\frac{3V}{2\pi a c}\right)c\right)^{1.6075} + (a c)^{1.6075}}{3}\right)^{\frac{1}{1.6075}}\right) + \pi\left(\frac{3V}{2\pi a c}\right)c \]

Bisected Axis of Semi Ellipsoid (a):

Volume of Semi Ellipsoid (V):

m³

Third Semi Axis of Semi Ellipsoid (c):

Total Surface Area of Semi Ellipsoid (TSA):

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1. What is Total Surface Area of Semi Ellipsoid?

The Total Surface Area of a Semi Ellipsoid refers to the complete area covering all surfaces of a half-ellipsoid shape. This includes both the curved surface and the elliptical base of the semi-ellipsoid.

2. How Does the Calculator Work?

The calculator uses the specialized formula:

Where:

\( TSA \) — Total Surface Area of Semi Ellipsoid (m²)
\( a \) — Bisected Axis of Semi Ellipsoid (m)
\( V \) — Volume of Semi Ellipsoid (m³)
\( c \) — Third Semi Axis of Semi Ellipsoid (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the total surface area by considering the geometric properties of a semi-ellipsoid, incorporating the bisected axis, volume, and third semi-axis.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of semi-ellipsoids is crucial in various engineering and architectural applications, including dome construction, tank design, and aerodynamic studies where these shapes are commonly used.

4. Using the Calculator

Tips: Enter the bisected axis (a), volume (V), and third semi-axis (c) in meters and cubic meters respectively. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the exponent 1.6075 used in the formula?
A: This specific exponent value is derived from mathematical modeling of ellipsoidal surfaces and provides an accurate approximation for surface area calculations.

Q3: Can this calculator be used for complete ellipsoids?
A: No, this calculator is specifically designed for semi-ellipsoids. For complete ellipsoids, a different formula would be required.

Q4: What are practical applications of semi-ellipsoids?
A: Semi-ellipsoidal shapes are commonly used in architecture (domes), engineering (tank ends), and product design due to their structural efficiency and aesthetic appeal.

Q5: How accurate is this calculation?
A: The calculation provides a mathematical approximation of the surface area. For critical applications, physical measurements or more precise computational methods may be necessary.