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

Total Surface Area of Torus Formula:

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

Total Surface Area of Torus:

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1. What is the Total Surface Area of Torus?

The Total Surface Area of a Torus is the complete area of the outer surface of the torus shape. A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the total surface area of a torus given its circular section radius and volume.

3. Importance of Torus Surface Area Calculation

Details: Calculating the surface area of a torus is important in various engineering and architectural applications, particularly in the design of ring-shaped structures, donut-shaped objects, and certain mechanical components.

4. Using the Calculator

Tips: Enter the radius of the circular section in meters and the volume of the torus in cubic meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What are some real-world examples of torus shapes?
A: Donuts, inner tubes, some types of life preservers, and certain architectural structures like circular arenas.

Q3: How is this formula derived?
A: The formula is derived from the geometric properties of a torus, using integration methods in calculus to determine both volume and surface area.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect torus shape with uniform circular cross-section and smooth surface.

Q5: Can this calculator handle different units?
A: The calculator uses meters for length and square meters for area. Convert your measurements to these units before calculation.