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Torus Volume Formula:
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A torus is a doughnut-shaped surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. It's commonly found in mathematics, physics, and engineering applications.
The calculator uses the Torus volume formula:
Where:
Explanation: The formula calculates the volume by multiplying the area of the cross-section (πr²) by the circumference of the path traced by the center of the cross-section (2πR).
Details: Calculating torus volume is important in various fields including architecture (designing circular structures), physics (magnetic field calculations in tokamaks), and manufacturing (designing rubber seals, tires, and other circular products).
Tips: Enter both radii in the same units. The major radius must be larger than the minor radius for a standard torus. Both values must be positive numbers.
Q1: What's the difference between major and minor radius?
A: The major radius (R) is the distance from the center of the tube to the center of the torus, while the minor radius (r) is the radius of the tube itself.
Q2: Can this formula be used for a horn torus or spindle torus?
A: No, this formula is specifically for a ring torus where R > r. Different formulas apply for horn (R = r) and spindle (R < r) tori.
Q3: What are some real-world examples of tori?
A: Common examples include doughnuts, lifebuoys, O-rings, and the shape of a fusion reactor (tokamak).
Q4: How is this related to surface area?
A: The surface area of a torus is calculated with a different formula: \( A = 4\pi^2 R r \).
Q5: What units should I use?
A: Any consistent units can be used (meters, inches, etc.), but all measurements must be in the same units.