Volume of Rhombicuboctahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ V = \frac{2}{3} \times (6 + 5\sqrt{2}) \times \left( \frac{3(9 + \sqrt{3})}{RA/V \times (6 + 5\sqrt{2})} \right)^3 \]

Volume of Rhombicuboctahedron:

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1. What is the Volume of Rhombicuboctahedron?

The Rhombicuboctahedron is an Archimedean solid with 8 triangular and 18 square faces. Its volume represents the total three-dimensional space enclosed by its surface, calculated based on its surface to volume ratio.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{2}{3} \times (6 + 5\sqrt{2}) \times \left( \frac{3(9 + \sqrt{3})}{RA/V \times (6 + 5\sqrt{2})} \right)^3 \]

Where:

\( V \) — Volume of Rhombicuboctahedron (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: This formula derives the volume from the surface to volume ratio using the geometric properties of the Rhombicuboctahedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, material science, and 3D modeling for determining capacity, density, and spatial requirements.

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 Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 26 faces (8 triangles and 18 squares), 24 vertices, and 48 edges.

Q2: What are typical surface to volume ratio values?
A: The surface to volume ratio depends on the size of the solid. Smaller objects have higher ratios while larger objects have lower ratios.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the base unit. For other units, appropriate conversion factors must be applied to the input values.

Q4: What are the applications of this calculation?
A: This calculation is useful in material science, nanotechnology, architecture, and any field dealing with three-dimensional geometric structures.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Rhombicuboctahedron shape and provides precise volume calculations.