Breadth of Torus given Radius and Total Surface Area Calculator

Breadth of Torus Given Radius and Total Surface Area Calculator

Formula Used:

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

Breadth of Torus:

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1. What is the Breadth of Torus?

The breadth of a 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:

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

Where:

\( b \) — Breadth of Torus (m)
\( r \) — Radius of Torus (m)
\( TSA \) — Total Surface Area of Torus (m²)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the breadth of a torus given its radius and total surface area, using the mathematical relationship between these geometric properties.

3. Importance of Torus 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, structural elements, and mechanical components.

4. Using the Calculator

Tips: Enter the radius of the torus and total surface area in meters and square meters respectively. 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 geometric shape that resembles 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 width of the torus, while diameter typically refers to the measurement through the center of the circular cross-section.

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

Q4: Are there limitations to this formula?
A: This formula assumes a perfect toroidal shape and may not be accurate for distorted or irregular toroidal forms.

Q5: Can this calculator be used for engineering design?
A: While this calculator provides theoretical values, actual engineering design should consider material properties, safety factors, and specific application requirements.