Hole Radius Of Torus Given Radius And Volume Calculator

Formula Used:

\[ r_{Hole} = r - \sqrt{\frac{V}{2\pi^2 r}} \]

Hole Radius of Torus (r_Hole):

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1. What is the Hole Radius of Torus?

The hole radius of a torus is the shortest distance from the center of the torus to the nearest point on the circumference of the circular cross-section. It represents the inner radius of the toroidal shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Hole} = r - \sqrt{\frac{V}{2\pi^2 r}} \]

Where:

\( r_{Hole} \) — Hole radius of torus (m)
\( r \) — Radius of torus (m)
\( V \) — Volume of torus (m³)
\( \pi \) — Archimedes' constant (≈ 3.14159)

Explanation: This formula calculates the hole radius based on the known overall radius and volume of the torus, using geometric relationships specific to toroidal shapes.

3. Importance of Hole Radius Calculation

Details: Calculating the hole radius is essential in engineering and architectural applications involving toroidal structures, as it determines the size of the central opening and affects the structural properties of the torus.

4. Using the Calculator

Tips: Enter the radius of the torus in meters and the volume in cubic meters. Both values must be positive numbers. The calculator will compute the corresponding hole radius.

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.

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

Q3: What are typical applications of torus calculations?
A: Torus calculations are used in various fields including architecture, engineering, physics (particularly in toroidal magnetic confinement devices), and computer graphics.

Q4: Can this formula be used for any torus size?
A: Yes, the formula is dimensionally consistent and can be applied to toruses of any size, as long as the input values are in consistent units.

Q5: What if I get a negative hole radius result?
A: A negative result would indicate invalid input values, as hole radius cannot be negative. Please verify that both radius and volume values are positive and physically meaningful.