Semi Minor Axis of Elliptic Cylinder given Surface to Volume Ratio Calculator

Formula Used:

\[ b = \frac{LSA}{\pi \times a \times \left( \left( \frac{RA}{V} \times h \right) - 2 \right)} \]

Lateral Surface Area of Elliptic Cylinder (LSA):

m²

Semi Major Axis of Elliptic Cylinder (a):

Surface to Volume Ratio of Elliptic Cylinder (RA/V):

1/m

Height of Elliptic Cylinder (h):

Semi Minor Axis of Elliptic Cylinder (b):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Semi Minor Axis of Elliptic 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 Elliptic Cylinder. It's a fundamental geometric parameter that defines the elliptical cross-section of the cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{LSA}{\pi \times a \times \left( \left( \frac{RA}{V} \times h \right) - 2 \right)} \]

Where:

\( b \) — Semi Minor Axis of Elliptic Cylinder (m)
\( LSA \) — Lateral Surface Area of Elliptic Cylinder (m²)
\( a \) — Semi Major Axis of Elliptic Cylinder (m)
\( \frac{RA}{V} \) — Surface to Volume Ratio of Elliptic Cylinder (1/m)
\( h \) — Height of Elliptic Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the semi minor axis by relating it to the lateral surface area, semi major axis, surface to volume ratio, and height of the elliptic cylinder.

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi minor axis is crucial for understanding the geometric properties of elliptic cylinders, which have applications in engineering, architecture, and various scientific fields where elliptical cross-sections are used.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length, square meters for area, and 1/meter for surface to volume ratio). Ensure all values are positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi major and semi minor axes?
A: The semi major axis is the longer radius of the ellipse, while the semi minor axis is the shorter radius. They define the elliptical shape of the cylinder's cross-section.

Q2: Can this formula be used for circular cylinders?
A: Yes, for circular cylinders where semi major axis equals semi minor axis (a = b), the formula simplifies accordingly.

Q3: What happens if the denominator becomes zero?
A: The calculation becomes undefined (division by zero). This occurs when (RA/V × h) - 2 = 0, which represents a specific geometric condition.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values. The accuracy depends on the precision of the input measurements.

Q5: What are typical applications of elliptic cylinders?
A: Elliptic cylinders are used in various engineering applications, architectural designs, fluid dynamics, and optical systems where elliptical cross-sections provide specific advantages over circular ones.