Volume Of Torus Given Radius Of Circular Section And Total Surface Area Calculator

Formula Used:

\[ V = 2\pi^2 r^2 \left( \frac{TSA}{4\pi^2 r} \right) \]

Volume of Torus:

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1. What is the Volume of Torus Formula?

The volume of a torus can be calculated using the formula that relates the radius of the circular section and the total surface area. This provides an alternative method to compute volume when surface area is known.

2. How Does the Calculator Work?

The calculator uses the derived formula:

\[ V = 2\pi^2 r^2 \left( \frac{TSA}{4\pi^2 r} \right) \]

Where:

\( V \) — Volume of Torus (m³)
\( r \) — Radius of Circular Section of Torus (m)
\( TSA \) — Total Surface Area of Torus (m²)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula is derived from the relationship between the volume and surface area of a torus, providing a direct calculation method when the circular section radius and total surface area are known.

3. Importance of Torus Volume Calculation

Details: Calculating the volume of a torus is important in various engineering and mathematical applications, including structural design, fluid dynamics, and geometric modeling.

4. Using the Calculator

Tips: Enter the radius of the circular section in meters and the total surface area in square meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a three-dimensional shape resembling a doughnut or inner tube, formed by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What are the typical applications of torus volume calculations?
A: Torus volume calculations are used in engineering (piping systems, structural elements), physics (magnetic field calculations), and various mathematical modeling applications.

Q3: How accurate is this calculation method?
A: The calculation is mathematically exact based on the derived formula, assuming precise input values and proper implementation of the mathematical operations.

Q4: Can this formula be used for partial torus sections?
A: No, this formula calculates the volume of a complete torus. Different formulas are required for partial torus sections.

Q5: What units should be used for input values?
A: The calculator expects meters for radius and square meters for surface area, but any consistent unit system can be used as long as both inputs use the same unit basis.