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The Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus. It represents the distance from the center of the circular cross-section to its outer edge.
The calculator uses the formula:
Where:
Explanation: This formula establishes an inverse relationship between the radius of the circular section and the surface to volume ratio of the torus.
Details: Calculating the radius of the circular section is crucial for understanding the geometry of a torus, designing toroidal objects, and solving problems in mathematics and engineering involving torus shapes.
Tips: Enter the surface to volume ratio of the torus in 1/m. The value must be valid and greater than zero.
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 surface to volume ratio defined for a torus?
A: The surface to volume ratio of a torus is the ratio of its total surface area to its volume, representing how much surface area is available per unit volume.
Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the specific dimensions of the torus. Smaller tori generally have higher surface to volume ratios.
Q4: Can this formula be used for any torus?
A: Yes, this formula applies to all tori and establishes the fundamental relationship between the circular section radius and the surface to volume ratio.
Q5: What are practical applications of this calculation?
A: This calculation is used in various fields including mechanical engineering (design of toroidal components), physics (magnetic field calculations), and architecture (design of toroidal structures).