Volume Of Torus Given Radius And Breadth Calculator

Volume of Torus Formula:

\[ V = 2\pi^2 r \left(\frac{b}{2} - r\right)^2 \]

Volume of Torus (V):

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1. What is the Volume of Torus Formula?

The volume of a torus is calculated using the formula \( V = 2\pi^2 r \left(\frac{b}{2} - r\right)^2 \), where r is the radius of the circular cross-section and b is the breadth of the torus. This formula provides the three-dimensional space occupied by the torus shape.

2. How Does the Calculator Work?

The calculator uses the torus volume formula:

\[ V = 2\pi^2 r \left(\frac{b}{2} - r\right)^2 \]

Where:

\( V \) — Volume of Torus (m³)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( r \) — Radius of Torus (m)
\( b \) — Breadth of Torus (m)

Explanation: The formula calculates the volume by considering the torus as a surface of revolution, where a circle is rotated around an axis external to the circle.

3. Importance of Volume Calculation

Details: Calculating the volume of a torus is important in various engineering and architectural applications, particularly in designing ring-shaped structures, piping systems, and mechanical components.

4. Using the Calculator

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

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 rotating a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What are the units for the inputs and output?
A: The inputs (radius and breadth) should be in meters, and the output (volume) will be in cubic meters.

Q3: Can this formula be used for any torus size?
A: Yes, the formula works for any torus size as long as the radius is smaller than half the breadth.

Q4: What if the radius is larger than half the breadth?
A: If the radius is larger than half the breadth, the formula would result in a negative value inside the square, which is mathematically invalid for a real torus.

Q5: Are there other ways to calculate torus volume?
A: Yes, the volume can also be calculated using the formula \( V = (\pi r^2)(2\pi R) \) where R is the distance from the center of the tube to the center of the torus.