Semi Minor Axis of Cut Cylinder given Volume and Short Height Calculator

Semi Minor Axis Formula:

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

Semi Minor Axis of Cut Cylinder (m):

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 the Cut Cylinder.

Purpose: It helps in determining the elliptical dimensions of a cut cylinder, which is important in various engineering and architectural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( b \) — Semi minor axis (meters)
\( r \) — Radius of cut cylinder (meters)
\( V \) — Volume of cut cylinder (cubic meters)
\( h_{short} \) — Short height of cut cylinder (meters)

Explanation: The formula calculates the semi minor axis based on the cylinder's radius, volume, and the short height of the cut.

3. Importance of Semi Minor Axis Calculation

Details: Accurate calculation of the semi minor axis is crucial for determining the exact shape and dimensions of the elliptical face of a cut cylinder.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between semi major and semi minor axis?
A: The semi major axis is half of the longest diameter of the ellipse, while the semi minor axis is half of the shortest diameter.

Q2: Why is there a ±5% tolerance?
A: The tolerance accounts for measurement uncertainties and practical variations in real-world applications.

Q3: Can this calculator be used for partially filled cylinders?
A: Yes, as long as the cut creates an elliptical face, this calculator can determine the semi minor axis.

Q4: What units should I use?
A: The calculator uses meters for length and cubic meters for volume, but any consistent unit system will work.

Q5: How precise are the results?
A: Results are precise to three decimal places, suitable for most engineering applications.