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

Formula Used:

\[ V = \pi \times h \times a \times \frac{TSA - LSA}{2 \pi a} \]

Height of Elliptic Cylinder:

Semi Major 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 Elliptic Cylinder is the total quantity of three dimensional space enclosed by the entire surface of the Elliptic Cylinder. It represents the capacity or the amount of material that can be contained within the cylinder.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \pi \times h \times a \times \frac{TSA - LSA}{2 \pi a} \]

Where:

\( V \) — Volume of Elliptic Cylinder (m³)
\( \pi \) — Archimedes' constant (≈3.1416)
\( h \) — Height of Elliptic Cylinder (m)
\( a \) — Semi Major Axis of Elliptic Cylinder (m)
\( TSA \) — Total Surface Area of Elliptic Cylinder (m²)
\( LSA \) — Lateral Surface Area of Elliptic Cylinder (m²)

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

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for determining the capacity of elliptic cylindrical containers, structural design calculations, and various engineering applications where precise volume measurements are required.

4. Using the Calculator

Tips: Enter all values in consistent units (meters for length, square meters for area). Ensure that the lateral surface area is less than the total surface area, and all values are 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 all surfaces (both elliptical bases and lateral curved surface), while lateral surface area only includes the curved surface area excluding the bases.

Q2: Can this formula be used for circular cylinders?
A: Yes, when the semi-major and semi-minor axes are equal (making the base circular), 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 structures, and fluid containers where elliptical shapes offer specific advantages.

Q4: How accurate is this calculation method?
A: The calculation is mathematically exact for perfect elliptic cylinders with the given parameters.

Q5: What units should I use for the inputs?
A: Use consistent units throughout - meters for length dimensions and square meters for area dimensions to get volume in cubic meters.