Semi Minor Axis of Cut Cylinder given Total Surface Area Calculator

Formula Used:

\[ b = \frac{TSA}{\pi \cdot r} - r - h_{Short} - h_{Long} \]

Total Surface Area of Cut Cylinder (TSA):

m²

Radius of Cut Cylinder (r):

Short Height of Cut Cylinder (h_Short):

Long Height of Cut Cylinder (h_Long):

Semi Minor Axis of Cut Cylinder (b):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 is a crucial geometric parameter in determining the elliptical cross-section of a cut cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{TSA}{\pi \cdot r} - r - h_{Short} - h_{Long} \]

Where:

\( b \) — Semi Minor Axis of Cut Cylinder (m)
\( TSA \) — Total Surface Area of Cut Cylinder (m²)
\( r \) — Radius of Cut Cylinder (m)
\( h_{Short} \) — Short Height of Cut Cylinder (m)
\( h_{Long} \) — Long Height of Cut Cylinder (m)
\( \pi \) — Archimedes' constant (≈3.141592653589793)

Explanation: This formula calculates the semi minor axis by considering the total surface area, radius, and both height measurements of the cut cylinder.

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi minor axis is essential for understanding the elliptical geometry of cut cylinders, which has applications in engineering, architecture, and various geometric calculations involving cylindrical sections.

4. Using the Calculator

Tips: Enter all values in meters. Ensure that Total Surface Area and Radius are positive values, and both heights are non-negative. The calculator provides results with six decimal places precision.

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 perpendicular to the major axis.

Q2: Can this calculator handle negative values?
A: No, all input values must be positive (except heights which can be zero). Negative values are not physically meaningful in this context.

Q3: What units should I use for input?
A: The calculator expects all measurements in meters for consistency. If you have measurements in other units, convert them to meters first.

Q4: How accurate is the calculation?
A: The calculation uses double-precision floating point arithmetic with results rounded to six decimal places, providing high accuracy for most practical applications.

Q5: What if I get a negative result for the semi minor axis?
A: A negative result indicates that the input values may not represent a physically possible cut cylinder configuration. Please verify your input values.