Radius Of Circular Section Of Torus Given Radius And Volume Calculator

Formula Used:

\[ r_{Circular\ Section} = \sqrt{\frac{V}{2\pi^2 r}} \]

Radius of Circular Section:

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1. What is the Radius of Circular Section of Torus?

The radius of circular section of a torus is the distance from the center of the circular cross-section to any point on its circumference. It represents the size of the tube that forms the torus shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Circular\ Section} = \sqrt{\frac{V}{2\pi^2 r}} \]

Where:

\( r_{Circular\ Section} \) — Radius of circular section (m)
\( V \) — Volume of torus (m³)
\( r \) — Radius of torus (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula derives from the volume formula of a torus and solves for the circular section radius.

3. Importance of Circular Section Radius Calculation

Details: Calculating the circular section radius is essential in engineering and architectural design where torus shapes are used, such as in piping systems, structural elements, and mechanical components.

4. Using the Calculator

Tips: Enter the volume of torus in cubic meters and the radius of torus 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 donut or inner tube, formed by revolving a circle in three-dimensional space about an axis.

Q2: How is the volume of a torus calculated?
A: The volume of a torus is calculated using the formula: \( V = 2\pi^2 R r^2 \), where R is the radius of the torus and r is the radius of the circular section.

Q3: What are typical applications of torus shapes?
A: Torus shapes are used in various applications including pipe fittings, tire tubes, nuclear fusion reactors (tokamaks), and architectural designs.

Q4: Can this calculator handle different units?
A: The calculator uses meters for length units. Convert other units to meters before calculation for accurate results.

Q5: What if I get an error or unexpected result?
A: Ensure both input values are positive numbers. The volume should be greater than zero and the radius should be sufficient to accommodate the given volume.