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Semi Minor Axis of Cut Cylinder given Lateral Surface Area and Total Surface Area Calculator

Semi Minor Axis Formula:

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

m²
m²
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1. What is Semi Minor Axis of Cut Cylinder?

Definition: The semi minor axis of a cut cylinder is half of the length of the longest chord perpendicular to the line joining the foci of the elliptic face.

Purpose: It helps in determining the dimensions of a cut cylinder when the total surface area, lateral surface area, and radius are known.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

  • \( b \) — Semi minor axis (meters)
  • \( TSA \) — Total surface area (m²)
  • \( LSA \) — Lateral surface area (m²)
  • \( r \) — Radius of cut cylinder (meters)
  • \( \pi \) — Pi constant (~3.1416)

Explanation: The formula calculates the semi minor axis by accounting for the difference between total and lateral surface areas, minus the base area.

3. Importance of Semi Minor Axis Calculation

Details: Accurate calculation ensures proper dimensional analysis of cut cylindrical objects in engineering and architectural applications.

4. Using the Calculator

Tips: Enter the total surface area, lateral surface area, radius, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the tolerance percentage for?
A: The tolerance (±5% by default) provides an acceptable range for the calculated semi minor axis to account for measurement uncertainties.

Q2: What units should I use?
A: Use consistent units (meters for length, square meters for area) for accurate results.

Q3: Can I use this for partially filled cylinders?
A: Yes, as long as the cut creates an elliptical face and you know the surface areas and radius.

Q4: What if my lateral surface area is greater than total surface area?
A: This would indicate invalid input values, as TSA should always be greater than LSA plus base area.

Q5: How precise are the results?
A: Results are displayed to 6 decimal places, but practical precision depends on input measurement accuracy.

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