Total Surface Area Of Semi Ellipsoid Given Volume Calculator

Total Surface Area of Semi Ellipsoid Formula:

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

Bisected Axis of Semi Ellipsoid (a):

Second Semi Axis of Semi Ellipsoid (b):

Volume of Semi Ellipsoid (V):

m³

Total Surface Area of Semi Ellipsoid (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Total Surface Area of Semi Ellipsoid?

The Total Surface Area of a Semi Ellipsoid represents the complete area covering all surfaces of a half ellipsoid. It includes both the curved surface and the elliptical base area.

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)
\( b \) — Second Semi Axis of Semi Ellipsoid (m)
\( V \) — Volume of Semi Ellipsoid (m³)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This complex formula calculates the surface area by considering the geometric properties of a semi-ellipsoid and its volume relationship.

3. Importance of Surface Area Calculation

Details: Surface area calculations are crucial in various engineering and architectural applications, including material estimation, heat transfer analysis, and structural design of domed structures.

4. Using the Calculator

Tips: Enter the bisected axis and second semi axis in meters, and volume in cubic meters. 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: How is this different from a full ellipsoid surface area?
A: The semi ellipsoid includes the curved surface area of half the ellipsoid plus the area of the elliptical cross-section where it was cut.

Q3: What are practical applications of this calculation?
A: This calculation is used in dome construction, architectural design, tank manufacturing, and any application involving half-ellipsoidal structures.

Q4: Why is the exponent 1.6075 used in the formula?
A: This specific exponent provides an accurate approximation for the surface area calculation of ellipsoidal shapes based on mathematical modeling.

Q5: Can this formula be used for any semi ellipsoid?
A: Yes, this formula applies to all semi ellipsoids as long as you have the correct measurements for the axes and volume.