Semi Major Axis of Elliptic Cylinder given Total Surface Area Calculator

Formula Used:

\[ a = \frac{TSA - LSA}{2 \pi b} \]

Total Surface Area of Elliptic Cylinder:

m²

Lateral Surface Area of Elliptic Cylinder:

m²

Semi Minor Axis of Elliptic Cylinder:

Semi Major Axis of Elliptic Cylinder:

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1. What is the Semi Major Axis of Elliptic Cylinder?

The Semi Major Axis of Elliptic Cylinder is the longest radius of elliptic face, as it begins in the center of the elliptic face, follows the major axis, and ends at the furthest edge-point. It is a fundamental parameter in defining the geometry of an elliptic cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a = \frac{TSA - LSA}{2 \pi b} \]

Where:

\( a \) — Semi Major Axis of Elliptic Cylinder (m)
\( TSA \) — Total Surface Area of Elliptic Cylinder (m²)
\( LSA \) — Lateral Surface Area of Elliptic Cylinder (m²)
\( b \) — Semi Minor Axis of Elliptic Cylinder (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: This formula derives the semi major axis from the difference between total and lateral surface areas, divided by the circumference of the elliptic base.

3. Importance of Semi Major Axis Calculation

Details: Calculating the semi major axis is essential for determining the complete geometric properties of an elliptic cylinder, including volume, surface area, and other dimensional characteristics in engineering and architectural applications.

4. Using the Calculator

Tips: Enter total surface area and lateral surface area in square meters, and semi minor axis in meters. All values must be positive numbers, with semi minor axis greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi major and semi minor axes?
A: The semi major axis is always equal to or longer than the semi minor axis in an ellipse. They define the elliptical cross-section of the cylinder.

Q2: Can this formula be used for circular cylinders?
A: Yes, for circular cylinders where semi major axis equals semi minor axis (a = b = radius), the formula simplifies accordingly.

Q3: What are typical units for these measurements?
A: While meters are standard, any consistent unit system can be used (cm, mm, inches, etc.) as long as all inputs use the same units.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. Accuracy depends on the precision of your measurements.

Q5: What if the lateral surface area is greater than total surface area?
A: This would result in a negative value, which is geometrically impossible. Please verify your input values.