Surface to Volume Ratio of Torus given Radius and Volume Calculator

Surface to Volume Ratio of Torus Formula:

\[ \text{Surface to Volume Ratio} = \frac{2}{\sqrt{\frac{V}{4\pi^2 r}}} \]

Surface to Volume Ratio:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Torus?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Surface to Volume Ratio} = \frac{2}{\sqrt{\frac{V}{4\pi^2 r}}} \]

Where:

\( V \) — Volume of the torus (m³)
\( r \) — Radius of the torus (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the ratio of surface area to volume for a torus given its volume and radius, using the mathematical constant pi and square root function.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is important in various fields including physics, engineering, and materials science. It affects heat transfer, chemical reaction rates, and other surface-dependent phenomena in toroidal structures.

4. Using the Calculator

Tips: Enter the volume of the torus in cubic meters and the radius in meters. Both values must be positive numbers greater than zero for accurate calculation.

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 units are used for the calculation?
A: The calculator uses meters for radius and cubic meters for volume, resulting in surface to volume ratio in meters⁻¹.

Q3: Can this calculator handle different unit systems?
A: The calculator requires consistent units. Convert all measurements to meters before calculation for accurate results.

Q4: What is the typical range of surface to volume ratios for tori?
A: The ratio varies depending on the dimensions, but generally ranges from very small values for large, thick tori to larger values for small, thin tori.

Q5: Are there practical applications of this calculation?
A: Yes, this calculation is used in engineering design, materials science, heat transfer analysis, and various physical applications involving toroidal shapes.