Volume of Elliptic Cylinder given Total Surface Area and Semi Minor Axis Calculator

Formula Used:

\[ V = \pi \times h \times b \times \frac{(TSA - LSA)}{2 \times \pi \times b} \]

Height of Elliptic Cylinder:

Semi Minor Axis of Elliptic Cylinder:

Total Surface Area of Elliptic Cylinder:

m²

Lateral Surface Area of Elliptic Cylinder:

m²

Volume of Elliptic Cylinder:

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1. What is the Volume of Elliptic Cylinder?

The volume of an elliptic cylinder represents the total three-dimensional space enclosed by its entire surface. It's calculated based on the cylinder's height and the dimensions of its elliptical base.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \pi \times h \times b \times \frac{(TSA - LSA)}{2 \times \pi \times b} \]

Where:

\( V \) — Volume of Elliptic Cylinder (m³)
\( h \) — Height of Elliptic Cylinder (m)
\( b \) — Semi Minor Axis of Elliptic Cylinder (m)
\( TSA \) — Total Surface Area of Elliptic Cylinder (m²)
\( LSA \) — Lateral Surface Area of Elliptic Cylinder (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the volume by utilizing the relationship between total surface area, lateral surface area, and the geometric properties of the elliptic cylinder.

3. Importance of Volume Calculation

Details: Calculating the volume of elliptic cylinders is essential in various engineering, architectural, and manufacturing applications where precise volume measurements are required for material estimation, capacity planning, and structural design.

4. Using the Calculator

Tips: Enter all measurements in consistent units (meters for length, square meters for area). Ensure that the total surface area is greater than the lateral surface area. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between total surface area and lateral surface area?
A: Total surface area includes both the lateral (curved) surface and the two elliptical bases, while lateral surface area only includes the curved surface.

Q2: Can this formula be used for circular cylinders?
A: Yes, for circular cylinders (where semi-minor axis equals semi-major axis), this formula simplifies to the standard cylinder volume formula.

Q3: What are typical applications of elliptic cylinders?
A: Elliptic cylinders are used in various engineering applications including pressure vessels, architectural elements, and mechanical components where elliptical shapes provide specific advantages.

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

Q5: What units should I use for the calculations?
A: Use consistent units throughout (meters for length, square meters for area). The calculator will output volume in cubic meters.