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

Semi Minor Axis Formula:

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

Radius of Cut Cylinder:

Long Height of Cut Cylinder:

Volume of Cut Cylinder:

m³

Tolerance:

Semi Minor Axis (b): m

Tolerance Range (±5%): 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 a cut cylinder.

Purpose: This calculator helps determine the semi minor axis when you know the volume, radius, and long height of a cut cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( b \) — Semi minor axis (meters)
\( r \) — Radius of cut cylinder (meters)
\( h_{long} \) — Long height of cut cylinder (meters)
\( V \) — Volume of cut cylinder (cubic meters)
\( \pi \) — Pi constant (~3.14159)

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi minor axis is essential 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, long height, and volume of the cut cylinder. The tolerance field (default ±5%) allows you to specify an acceptable range for the result.

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cylinder?
A: A cut cylinder is a cylinder that has been sliced by a plane, resulting in an elliptical cross-section at the cut.

Q2: How is the long height different from short height?
A: The long height is the maximum vertical distance on one side, while the short height is the minimum vertical distance on the opposite side.

Q3: Why include a tolerance field?
A: The tolerance field helps account for measurement uncertainties and practical construction tolerances.

Q4: Can this calculator be used for partially filled cylinders?
A: Yes, if you know the volume of liquid and the dimensions, you can calculate the semi minor axis of the liquid surface.

Q5: What units should I use?
A: The calculator uses meters for length and cubic meters for volume, but any consistent unit system will work.