Surface to Volume Ratio of Torus Formula:
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The Surface to Volume Ratio of a Torus is a geometric measurement that represents the relationship between the total surface area and the volume of a torus shape. It indicates how much surface area is available per unit volume of the torus.
The calculator uses the formula:
Where:
Explanation: This formula calculates the ratio of surface area to volume for a torus given its total surface area and radius.
Details: The surface to volume ratio is important in various fields including material science, heat transfer, and biological systems. For toroidal shapes, this ratio helps in understanding properties like heat dissipation, chemical reactivity, and structural efficiency.
Tips: Enter the total surface area in square meters and the radius in meters. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is a torus?
A: A torus is a three-dimensional shape resembling a doughnut or inner tube, formed by revolving a circle in three-dimensional space about an axis coplanar with the circle.
Q2: What units are used for surface to volume ratio?
A: The surface to volume ratio is typically measured in reciprocal meters (m⁻¹), representing square meters of surface area per cubic meter of volume.
Q3: How does radius affect the surface to volume ratio?
A: For a given surface area, increasing the radius generally decreases the surface to volume ratio, as volume increases more rapidly than surface area with increasing size.
Q4: What are practical applications of torus surface to volume ratio?
A: This calculation is useful in engineering designs involving toroidal shapes, such as in nuclear fusion reactors (tokamaks), certain types of heat exchangers, and architectural structures.
Q5: Can this formula be used for partial torus sections?
A: No, this formula is specifically for complete torus shapes. Partial torus sections require different calculations based on the specific geometry.