Semi Minor Axis of Cut Cylinder Calculator

Formula Used:

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

Radius of Cut Cylinder (r):

Long Height of Cut Cylinder (h_Long):

Short Height of Cut Cylinder (h_Short):

Semi Minor Axis of Cut Cylinder (b):

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

The Semi Minor Axis of a Cut Cylinder is half of the length of the shortest diameter of the elliptical face formed when a cylinder is cut by an inclined plane. It represents the distance from the center to the edge along the minor axis of the ellipse.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( b \) — Semi Minor Axis of Cut Cylinder (m)
\( r \) — Radius of Cut Cylinder (m)
\( h_{Long} \) — Long Height of Cut Cylinder (m)
\( h_{Short} \) — Short Height of Cut Cylinder (m)

Explanation: This formula calculates the semi minor axis by considering the radius of the original cylinder and the height difference between the longest and shortest sides of the cut.

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi minor axis is essential for understanding the geometry of cut cylinders, which is important in various engineering applications, architectural designs, and manufacturing processes where cylindrical objects are cut at angles.

4. Using the Calculator

Tips: Enter the radius in meters, long height in meters, and short height in meters. All values must be positive, and the long height must be greater than the short height.

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: Can this formula be used for any cut angle?
A: This specific formula applies to cylinders cut by a plane that creates an elliptical cross-section. The angle is determined by the height difference.

Q3: What units should I use for the inputs?
A: The calculator uses meters, but you can use any consistent unit of length as long as all measurements are in the same unit.

Q4: What if the long height is not greater than the short height?
A: The calculation requires that the long height be greater than the short height. If they are equal, the cut would be parallel to the base and the cross-section would be circular, not elliptical.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect cylinder cut by a perfect plane. Real-world measurements may introduce some error.