Radius of Cut Cylinder given Semi Minor Axis Calculator

Formula Used:

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

Semi Minor Axis of Cut Cylinder (b):

Long Height of Cut Cylinder (h_Long):

Short Height of Cut Cylinder (h_Short):

Radius of Cut Cylinder (r):

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

The formula calculates the radius of a cut cylinder using the semi-minor axis and the difference between the long and short heights. It's derived from geometric relationships in a cut cylinder where the top surface is elliptical.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the radius by applying the Pythagorean theorem to the geometric configuration of the cut cylinder, where the height difference creates a right triangle relationship with the semi-minor axis.

3. Importance of Radius Calculation

Details: Calculating the radius of a cut cylinder is essential for determining various geometric properties, volume calculations, and practical applications in engineering and design where cylindrical sections are cut at an angle.

4. Using the Calculator

Tips: Enter semi-minor axis and both height values in meters. All values must be positive, and the long height must be greater than the short height. The calculator will compute the radius using the geometric relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is a cut cylinder?
A: A cut cylinder is a cylindrical shape that has been sliced by a plane that is not parallel to the base, resulting in an elliptical top surface.

Q2: Why is the height difference divided by 2 in the formula?
A: The height difference represents the total vertical displacement across the diameter, so half of this value corresponds to the vertical displacement from the center to the edge.

Q3: What units should be used for input values?
A: The calculator uses meters for all measurements, but any consistent unit system can be used as long as all inputs are in the same units.

Q4: Can this formula be used for any cut angle?
A: This specific formula applies when the cut plane creates an elliptical cross-section, which occurs when the cut is oblique to the cylinder's axis but not parallel to it.

Q5: What if the calculated radius is imaginary?
A: If the expression under the square root becomes negative, it indicates that the input values are not geometrically possible for a cut cylinder with the given parameters.