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

Formula Used:

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

Radius of Cut Cylinder (r):

Long Height of Cut Cylinder (h_Long):

Lateral Surface Area of Cut Cylinder (LSA):

m²

Semi Minor Axis of Cut Cylinder (b):

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1. What is Semi Minor Axis of Cut Cylinder?

The Semi Minor Axis of Cut Cylinder is the half of the length of the longest chord which is perpendicular to the line joining the foci of the elliptic face of the Cut Cylinder. It represents the shorter radius of the elliptical cross-section formed when a cylinder is cut by an inclined plane.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( b \) — Semi Minor Axis of Cut Cylinder (m)
\( r \) — Radius of Cut Cylinder (m)
\( h_{Long} \) — Long Height of Cut Cylinder (m)
\( LSA \) — Lateral Surface Area of Cut Cylinder (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the semi minor axis by considering the geometric relationship between the cylinder's radius, the longer height measurement, and its lateral surface area when cut by an inclined plane.

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. This measurement is essential in various engineering applications, architectural designs, and manufacturing processes where cylindrical objects are cut at angles, helping determine the precise dimensions and properties of the resulting elliptical face.

4. Using the Calculator

Tips: Enter the radius in meters, long height in meters, and lateral surface area in square meters. All values must be positive numbers greater than zero. Ensure accurate measurements for precise results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between semi major and semi minor axis?
A: The semi major axis is the longer radius of the ellipse, while the semi minor axis is the shorter radius. Both are perpendicular to each other at the center of the ellipse.

Q2: Can this calculator be used for any type of cylinder cut?
A: This calculator is specifically designed for cylinders cut by a single inclined plane, resulting in an elliptical cross-section.

Q3: What units should I use for input values?
A: The calculator uses meters for length measurements and square meters for area. Ensure consistent units for accurate results.

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

Q5: What if I get an error or unexpected result?
A: Double-check that all input values are positive numbers and that the lateral surface area value is physically possible given the radius and height measurements.