Total Surface Area of Rhombicuboctahedron given Surface to Volume Ratio Calculator

Formula Used:

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

Total Surface Area (TSA):

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1. What is the Total Surface Area of Rhombicuboctahedron?

The Total Surface Area of a Rhombicuboctahedron is the total quantity of plane enclosed by the entire surface of this Archimedean solid. It consists of 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( TSA \) — Total Surface Area (m²)
\( RA/V \) — Surface to Volume Ratio (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula derives the surface area from the surface to volume ratio using the geometric properties of the rhombicuboctahedron.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material science, architectural design, and understanding the geometric properties of this polyhedron. It helps in determining coating requirements, heat transfer properties, and structural characteristics.

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 8 triangular faces and 18 square faces, totaling 26 faces, 24 vertices, and 48 edges.

Q2: Why is surface to volume ratio important?
A: Surface to volume ratio is a critical parameter that affects many physical and chemical properties, including reaction rates, heat dissipation, and material strength.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size and specific geometry, but generally decreases as the size of the object increases.

Q4: 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.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the rhombicuboctahedron, assuming precise input values.