Total Surface Area of Rhombicuboctahedron given Volume Calculator

Formula Used:

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

Total Surface Area of Rhombicuboctahedron:

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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:

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

Where:

\( TSA \) — Total Surface Area of Rhombicuboctahedron (m²)
\( V \) — Volume of Rhombicuboctahedron (m³)
\( \sqrt{3} \) — 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 volume by first finding the edge length and then calculating the total surface area.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is important in various fields including architecture, materials science, and engineering for determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the volume of the Rhombicuboctahedron in cubic meters. The value must be positive and greater than zero.

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.

Q2: How many edges and vertices does a Rhombicuboctahedron have?
A: It has 48 edges and 24 vertices.

Q3: What are practical applications of this calculation?
A: This calculation is useful in architecture, crystallography, and materials engineering where this specific polyhedral shape appears.

Q4: Can this formula be used for any Rhombicuboctahedron?
A: Yes, this formula works for any regular Rhombicuboctahedron where all edges are equal in length.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise, though practical measurements of volume may introduce some error in real-world applications.