1. What is the Breadth of Torus Formula?

The formula calculates the breadth of a torus given its radius and volume. The torus is a three-dimensional shape formed by rotating a circle in three-dimensional space about an axis coplanar with the circle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Breadth of Torus (m)
• \( r \) — Radius of Torus (m)
• \( V \) — Volume of Torus (m³)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives from the relationship between the torus dimensions and its volume, incorporating the square root function to solve for breadth.

3. Importance of Torus Breadth Calculation

Details: Calculating the breadth of a torus is essential in various engineering and architectural applications, particularly in designing circular structures, piping systems, and mechanical components with toroidal shapes.

4. Using the Calculator

Tips: Enter the radius of the torus in meters and the volume in cubic meters. Both values must be positive numbers. The calculator will compute the breadth of the torus.

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use for inputs?
A: Use consistent units, typically meters for radius and cubic meters for volume. The result will be in meters.

Q3: Can this formula be used for partial torus shapes?
A: No, this formula applies only to complete, circular torus shapes.

Q4: What if I get an error or unexpected result?
A: Ensure all input values are positive numbers and that the volume is physically possible for the given radius.

Q5: Are there limitations to this formula?
A: This formula assumes a perfect circular torus shape and may not be accurate for deformed or non-uniform toroidal shapes.