Breadth of Torus given Radius of Circular Section and Volume Calculator

Formula Used:

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

Breadth of Torus:

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1. What is the Breadth of Torus Formula?

The Breadth of Torus formula calculates the horizontal distance from the leftmost point to the rightmost point of a torus given its volume and the radius of its circular cross-section. This measurement is essential in understanding the spatial dimensions of toroidal shapes.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( Volume\ of\ Torus \) — Total volume of the torus (m³)
\( Radius\ of\ Circular\ Section\ of\ Torus \) — Radius of the circular cross-section (m)
\( \pi \) — Mathematical constant approximately equal to 3.14159

Explanation: The formula derives the breadth by first calculating the major radius from the volume and minor radius, then adding the minor radius and doubling the result.

3. Importance of Torus Breadth Calculation

Details: Calculating the breadth of a torus is crucial in engineering, architecture, and manufacturing where toroidal shapes are used. It helps in determining the spatial requirements and proper fitting of torus-shaped objects.

4. Using the Calculator

Tips: Enter the volume of the torus in cubic meters and the radius of the circular section in 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: How is the breadth of a torus different from its diameter?
A: The breadth of a torus is the total width including the hole, which is equivalent to twice the sum of the major radius and minor radius.

Q3: What are typical applications of torus shapes?
A: Torus shapes are used in various applications including magnetic coils, architectural designs, tire tubes, and certain types of pressure vessels.

Q4: Can this formula be used for partial torus sections?
A: No, this formula is specifically for complete, symmetrical torus shapes with circular cross-sections.

Q5: What units should be used for input values?
A: The calculator uses meters for length measurements and cubic meters for volume. Ensure consistent units for accurate results.