Volume of Truncated Cuboctahedron Given Surface to Volume Ratio Calculator

Formula Used:

\[ V = 2 \times (11 + 7\sqrt{2}) \times \left( \frac{6(2 + \sqrt{2} + \sqrt{3})}{RA/V \times (11 + 7\sqrt{2})} \right)^3 \]

Volume of Truncated Cuboctahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Truncated Cuboctahedron?

The Volume of Truncated Cuboctahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Cuboctahedron. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = 2 \times (11 + 7\sqrt{2}) \times \left( \frac{6(2 + \sqrt{2} + \sqrt{3})}{RA/V \times (11 + 7\sqrt{2})} \right)^3 \]

Where:

\( V \) — Volume of Truncated Cuboctahedron (m³)
\( RA/V \) — Surface to Volume Ratio (1/m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{3} \) — Square root of 3 (approximately 1.7321)

Explanation: The formula calculates the volume based on the given surface to volume ratio, using the mathematical properties of the truncated cuboctahedron shape.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, physics, engineering, and architecture. It helps in determining capacity, material requirements, and structural properties.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Cuboctahedron?
A: A truncated cuboctahedron is an Archimedean solid with 26 faces: 12 squares, 8 regular hexagons, and 6 regular octagons.

Q2: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size of the truncated cuboctahedron. Smaller objects have higher surface to volume ratios.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the base unit. Ensure consistent units when inputting values and interpreting results.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most engineering and mathematical applications.

Q5: Are there limitations to this calculation?
A: The formula assumes a perfect geometric shape. Real-world objects may have manufacturing tolerances that affect the actual volume.