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

Semi Minor Axis Formula:

\[ b = \sqrt{r^2+\left(\frac{\frac{LSA}{\pi r}-2h_{short}}{2}\right)^2} \]

Semi Minor Axis:

1. What is Semi Minor Axis of Cut Cylinder?

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

Purpose: It helps in determining the elliptical dimensions of a cylinder that has been cut by an inclined plane.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \sqrt{r^2+\left(\frac{\frac{LSA}{\pi r}-2h_{short}}{2}\right)^2} \]

Where:

\( b \) — Semi minor axis
\( r \) — Radius of the cut cylinder
\( LSA \) — Lateral surface area
\( h_{short} \) — Short height of the cut cylinder

Explanation: The formula calculates the semi minor axis using the radius, lateral surface area, and the short height of the cut cylinder.

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi minor axis is crucial for understanding the elliptical cross-section of a cut cylinder, which is important in engineering and architectural applications.

4. Using the Calculator

Tips: Enter the radius, lateral surface area, and short height of the cut cylinder. All values must be > 0. The ±5% indicates the acceptable tolerance range for inputs.

5. Frequently Asked Questions (FAQ)

Q1: What does ±5% mean in the input fields?
A: It indicates that the calculator accounts for a 5% tolerance in the input values, which is common in engineering measurements.

Q2: How is the lateral surface area measured?
A: The lateral surface area is the total area of the curved surface of the cut cylinder, excluding the top and bottom faces.

Q3: What's the difference between short height and long height?
A: The short height is the minimum vertical distance, while the long height is the maximum vertical distance on the cut cylinder.

Q4: Can this calculator be used for partially filled cylinders?
A: Yes, if the partial filling creates an elliptical cross-section, this calculator can determine the semi minor axis.

Q5: What units should I use?
A: Use consistent units (e.g., all in meters or all in inches) for accurate results.