Semi Minor Axis of Elliptic Cylinder given Volume Calculator

Formula Used:

\[ b = \frac{V}{\pi \cdot h \cdot a} \]

Volume of Elliptic Cylinder (V):

m³

Height of Elliptic Cylinder (h):

Semi Major Axis of Elliptic Cylinder (a):

Semi Minor Axis of Elliptic Cylinder (b):

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

The Semi Minor Axis of an Elliptic Cylinder is half of the length of the shortest diameter of the elliptical cross-section. It is perpendicular to the semi-major axis and helps define the elliptical shape of the cylinder's base.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \frac{V}{\pi \cdot h \cdot a} \]

Where:

\( b \) — Semi Minor Axis of Elliptic Cylinder (m)
\( V \) — Volume of Elliptic Cylinder (m³)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( h \) — Height of Elliptic Cylinder (m)
\( a \) — Semi Major Axis of Elliptic Cylinder (m)

Explanation: This formula rearranges the volume formula for an elliptic cylinder to solve for the semi-minor axis when volume, height, and semi-major axis are known.

3. Importance of Semi Minor Axis Calculation

Details: Calculating the semi-minor axis is essential for understanding the complete geometry of an elliptic cylinder. It helps in various engineering and architectural applications where precise dimensional calculations are required.

4. Using the Calculator

Tips: Enter volume in cubic meters, height in meters, and semi-major axis in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi-minor and semi-major axes?
A: The semi-minor axis is always perpendicular to the semi-major axis and is the shorter of the two axes that define the elliptical cross-section.

Q2: Can this formula be used for any elliptic cylinder?
A: Yes, this formula applies to all right elliptic cylinders where the height is perpendicular to the elliptical base.

Q3: What are typical units for these measurements?
A: While meters are used here, any consistent unit system can be used (cm, mm, inches, etc.) as long as all inputs use the same units.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and using the exact value of pi in calculations.

Q5: What if I have the semi-minor axis and need to find volume?
A: You would use the standard volume formula: \( V = \pi \cdot a \cdot b \cdot h \), where a is semi-major axis and b is semi-minor axis.