Volume Of Torus Given Radius And Total Surface Area Calculator

Formula Used:

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

Volume of Torus (V):

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1. What is the Volume of Torus Calculation?

The volume of a torus calculation determines the three-dimensional space occupied by a torus (doughnut-shaped object) given its radius and total surface area. This is important in geometry and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula derives the volume from the given radius and total surface area using geometric relationships specific to torus shapes.

3. Importance of Torus Volume Calculation

Details: Calculating torus volume is essential in various fields including mechanical engineering, architecture, and physics where toroidal shapes are encountered in designs and natural phenomena.

4. Using the Calculator

Tips: Enter the radius of the torus in meters and the total surface area in square meters. Both values must be positive numbers greater than zero.

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 typical applications of torus volume calculations?
A: Torus volume calculations are used in designing mechanical components, architectural structures, and in physics for calculating volumes of toroidal objects.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for perfect torus shapes, assuming accurate input values and proper application of the formula.

Q4: Can this calculator handle different units?
A: The calculator uses meters for radius and square meters for surface area. Convert other units to these standard units before calculation.

Q5: What if I get an unexpected result?
A: Double-check your input values and ensure they are positive numbers. The radius and surface area must be compatible for a valid torus geometry.