Hole Radius Of Torus Given Radius Of Circular Section And Volume Calculator

Formula Used:

\[ \text{Hole Radius of Torus} = \left( \frac{\text{Volume of Torus}}{2 \times \pi^2 \times (\text{Radius of Circular Section of Torus})^2} \right) - \text{Radius of Circular Section of Torus} \]

Hole Radius of Torus:

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1. What is the Hole Radius of Torus Formula?

The Hole Radius of Torus formula calculates the distance from the center of the torus to the nearest point on the circumference of the circular cross-section, given the volume and the radius of the circular section.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Hole Radius} = \left( \frac{V}{2 \times \pi^2 \times r^2} \right) - r \]

Where:

\( V \) — Volume of the torus (m³)
\( r \) — Radius of the circular section (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives from the volume formula of a torus and solves for the hole radius.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius is essential in geometry and engineering applications where torus-shaped objects are used, such as in design and manufacturing.

4. Using the Calculator

Tips: Enter the volume of the torus in cubic meters and the radius of the circular section in meters. Both values must be positive.

5. Frequently Asked Questions (FAQ)

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

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

Q3: Can the hole radius be negative?
A: No, the hole radius should be a positive value. If the calculation results in a negative value, check the input values for errors.

Q4: What if the volume is too small for the given radius?
A: The formula requires that the volume is sufficient to form a torus with the given circular section radius. Otherwise, the result may not be meaningful.

Q5: Is this formula applicable to all torus shapes?
A: This formula applies to a standard torus where the circular cross-section is consistent throughout.