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

Total Surface Area of Torus Formula:

\[ TSA = 4 \times \pi^2 \times r_{Circular\ Section} \times (r_{Hole} + r_{Circular\ Section}) \]

Total Surface Area of Torus (TSA):

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1. What is the Total Surface Area of Torus?

The Total Surface Area of a Torus is the complete area covering the entire 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 torus surface area formula:

\[ TSA = 4 \times \pi^2 \times r_{Circular\ Section} \times (r_{Hole} + r_{Circular\ Section}) \]

Where:

\( TSA \) — Total Surface Area of Torus (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( r_{Circular\ Section} \) — Radius of circular section of torus (m)
\( r_{Hole} \) — Hole radius of torus (m)

Explanation: The formula calculates the total surface area by considering both the major radius (hole radius + circular section radius) and the minor radius (circular section radius) of the torus.

3. Importance of Torus Surface Area Calculation

Details: Calculating the surface area of a torus is important in various engineering applications, architectural designs, manufacturing processes, and mathematical modeling where torus-shaped objects are involved.

4. Using the Calculator

Tips: Enter the radius of the circular section and the hole radius in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: What are the practical applications of torus surface area calculation?
A: Torus surface area calculations are used in designing doughnut-shaped objects, architectural structures, mechanical components, and in various engineering applications.

Q3: How does the hole radius affect the surface area?
A: The surface area increases as the hole radius increases, given a constant circular section radius, because the overall size of the torus becomes larger.

Q4: Can this formula be used for partial torus surfaces?
A: No, this formula calculates the total surface area of a complete torus. For partial torus surfaces, different calculations are required.

Q5: What units should be used for the inputs?
A: The calculator uses meters for both radius inputs, but the formula works with any consistent unit system as long as both radii are in the same units.