Volume of Rhombicuboctahedron given Total Surface Area Calculator

Formula Used:

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

Volume of Rhombicuboctahedron:

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1. What is the Volume of Rhombicuboctahedron?

The Volume of Rhombicuboctahedron is the total quantity of three dimensional space enclosed by the surface of the Rhombicuboctahedron. It is an Archimedean solid with 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Rhombicuboctahedron (m³)
\( TSA \) — Total Surface Area of Rhombicuboctahedron (m²)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{3} \) — Square root of 3 (approximately 1.7321)

Explanation: This formula derives the volume from the total surface area by first calculating the edge length and then applying the volume formula for a 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. It helps in determining capacity, material requirements, and spatial relationships.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding volume in cubic meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 26 faces - 8 equilateral triangles and 18 squares. It has 24 identical vertices and 48 edges.

Q2: Why is the formula so complex?
A: The formula complexity arises from the geometric relationships between surface area, edge length, and volume in this particular polyhedron. The constants come from mathematical derivations involving square roots.

Q3: Can this calculator handle different units?
A: The calculator assumes input in square meters and outputs volume in cubic meters. For other units, convert your surface area measurement to square meters first.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications involving geometric calculations.

Q5: Are there any limitations to this calculation?
A: The formula assumes a perfect Rhombicuboctahedron shape. For irregular or deformed shapes, more complex calculations or 3D scanning methods would be required.