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

Formula Used:

\[ Breadth\ of\ Torus = 2 \times \left( \left( \frac{Total\ Surface\ Area\ of\ Torus}{4\pi^2 \times Radius\ of\ Circular\ Section\ of\ Torus} \right) + Radius\ of\ Circular\ Section\ of\ Torus \right) \]

Breadth of Torus:

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1. What is the Breadth of Torus?

The Breadth of Torus is defined as the horizontal distance from the leftmost point to the rightmost point of the Torus. It represents the overall width of the toroidal shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Breadth\ of\ Torus = 2 \times \left( \left( \frac{Total\ Surface\ Area}{4\pi^2 \times Radius\ of\ Circular\ Section} \right) + Radius\ of\ Circular\ Section \right) \]

Where:

\( Total\ Surface\ Area \) — Total surface area of the torus (m²)
\( Radius\ of\ Circular\ Section \) — Radius of the circular cross-section of the torus (m)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: The formula calculates the breadth by considering both the surface area and the radius of the circular section, incorporating the mathematical constant π.

3. Importance of Breadth Calculation

Details: Calculating the breadth of a torus is important in various engineering and architectural applications where toroidal shapes are used, such as in pipe systems, architectural designs, and mechanical components.

4. Using the Calculator

Tips: Enter the total surface area in square meters and the radius of the circular section in 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: How is the breadth different from the diameter?
A: The breadth specifically refers to the horizontal measurement from the leftmost to rightmost points, while diameter typically refers to the distance through the center.

Q3: What are typical applications of torus shapes?
A: Torus shapes are used in various applications including magnetic confinement fusion devices (tokamaks), pipe fittings, architectural elements, and jewelry design.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect toroidal shape with uniform circular cross-section and may not be accurate for irregular or deformed toroidal shapes.

Q5: Can this formula be used for hollow torus shapes?
A: Yes, the formula works for both solid and hollow torus shapes as long as the surface area and circular section radius are properly measured.