Radius of Circular Section of Torus Calculator

Formula Used:

\[ \text{Radius of Circular Section of Torus} = \text{Radius of Torus} - \text{Hole Radius of Torus} \] \[ r_{\text{Circular Section}} = r - r_{\text{Hole}} \]

Radius of Circular Section of Torus:

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

The Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus. It represents the distance from the center of the torus tube to its outer surface.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Radius of Circular Section of Torus} = \text{Radius of Torus} - \text{Hole Radius of Torus} \] \[ r_{\text{Circular Section}} = r - r_{\text{Hole}} \]

Where:

\( r_{\text{Circular Section}} \) — Radius of Circular Section of Torus (m)
\( r \) — Radius of Torus (m)
\( r_{\text{Hole}} \) — Hole Radius of Torus (m)

Explanation: The formula calculates the radius of the circular cross-section by subtracting the hole radius from the overall torus radius.

3. Importance of Radius Calculation

Details: Calculating the radius of the circular section is essential for understanding the geometry of a torus, which is important in various engineering, architectural, and mathematical applications involving toroidal shapes.

4. Using the Calculator

Tips: Enter the Radius of Torus and Hole Radius of Torus in meters. Both values must be positive, and the Radius of Torus must be greater than the Hole Radius of Torus.

5. Frequently Asked Questions (FAQ)

Q1: What is a Torus?
A: A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What are the practical applications of torus geometry?
A: Torus shapes are used in various fields including architecture (donut-shaped buildings), engineering (torus-shaped vessels), mathematics, and physics (magnetic confinement in fusion reactors).

Q3: Can the Hole Radius be larger than the Radius of Torus?
A: No, the Hole Radius must be smaller than the Radius of Torus for a valid torus geometry. If they are equal, the torus degenerates into a single point.

Q4: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as both inputs use the same unit.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect torus geometry. The accuracy depends on the precision of your input measurements.