Hole Radius of Torus given Radius and Breadth Calculator

Formula Used:

\[ \text{Hole Radius of Torus} = \text{Radius of Torus} - \left( \frac{\text{Breadth of Torus}}{2} - \text{Radius of Torus} \right) \] \[ r_{\text{Hole}} = r - \left( \frac{b}{2} - r \right) \]

Hole Radius of Torus:

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1. What is Hole Radius of Torus?

The Hole Radius of Torus is the shortest line connecting the center of the Torus to the nearest point on the circumference of the circular cross-section of the Torus. It represents the distance from the center of the torus to the inner edge of its ring structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{\text{Hole}} = r - \left( \frac{b}{2} - r \right) \]

Where:

\( r_{\text{Hole}} \) — Hole Radius of Torus (m)
\( r \) — Radius of Torus (m)
\( b \) — Breadth of Torus (m)

Explanation: The formula calculates the hole radius by subtracting the difference between half the breadth and the radius from the radius itself.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius is essential in geometry and engineering applications involving toroidal shapes. It helps determine the inner dimensions of torus-shaped objects, which is crucial for manufacturing, structural design, and various mathematical computations.

4. Using the Calculator

Tips: Enter the radius of torus and breadth of torus in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Torus?
A: A torus is a three-dimensional geometric shape that resembles a doughnut or an inner tube. It's a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: How is Breadth of Torus defined?
A: Breadth of Torus is defined as the horizontal distance from the leftmost point to the rightmost point of the Torus when viewed from a specific orientation.

Q3: What are typical applications of torus geometry?
A: Torus geometry is used in various fields including architecture (domes and arches), engineering (pipes and rings), physics (magnetic confinement in fusion reactors), and mathematics (topology and geometry studies).

Q4: Can the hole radius be negative?
A: No, the hole radius cannot be negative as it represents a physical distance. If the calculation results in a negative value, it indicates that the input values may not represent a valid torus geometry.

Q5: How does this relate to the major and minor radii?
A: In torus geometry, the radius of torus (r) is typically the minor radius (radius of the tube), while the hole radius helps determine the major radius (distance from the center of the tube to the center of the torus).