Hole Radius Of Torus Given Radius And Surface To Volume Ratio Calculator

Formula Used:

\[ \text{Hole Radius of Torus} = \text{Radius of Torus} - \left( \frac{2}{\text{Surface to Volume Ratio of Torus}} \right) \]

Hole Radius of Torus:

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1. What is the 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 to the inner edge of the toroidal shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Hole Radius of Torus} = \text{Radius of Torus} - \left( \frac{2}{\text{Surface to Volume Ratio of Torus}} \right) \]

Where:

Radius of Torus - The line connecting the center of the overall Torus to the center of a circular cross-section of the Torus (in meters)
Surface to Volume Ratio of Torus - The numerical ratio of the total surface area of Torus to the volume of the Torus (in 1/m)

Explanation: This formula calculates the hole radius based on the overall radius of the torus and its surface to volume ratio, providing the distance from the center to the inner edge of the toroidal shape.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius of a torus is important in various engineering and mathematical applications, particularly in geometry, architecture, and mechanical design where toroidal shapes are used.

4. Using the Calculator

Tips: Enter the radius of torus in meters and the surface to volume ratio in 1/m. 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 inner tube, formed by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: How is the hole radius different from the radius of torus?
A: The radius of torus refers to the distance from the center of the entire torus to the center of the circular cross-section, while the hole radius is the distance from the center to the inner edge of the torus.

Q3: What are typical applications of torus calculations?
A: Torus calculations are used in various fields including architecture (designing arches and domes), engineering (designing pipes and rings), physics (magnetic field calculations), and mathematics (geometric modeling).

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 an error in the input parameters.

Q5: How does surface to volume ratio affect the hole radius?
A: A higher surface to volume ratio typically results in a smaller hole radius, as the torus becomes "thinner" relative to its overall size.