Total Surface Area of Snub Cube given Surface to Volume Ratio Calculator

Formula Used:

\[ TSA = 2 \times (3 + 4 \times \sqrt{3}) \times \left( \frac{2 \times (3 + 4 \times \sqrt{3})}{RA/V \times \frac{3 \times \sqrt{[Tribonacci_C] - 1} + 4 \times \sqrt{[Tribonacci_C] + 1}}{3 \times \sqrt{2 - [Tribonacci_C]}}} \right)^2 \]

Total Surface Area (TSA):

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1. What is the Total Surface Area of Snub Cube?

The Total Surface Area of a Snub Cube is the total quantity of plane enclosed by the entire surface of this Archimedean solid. It represents the sum of the areas of all its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( TSA \) — Total Surface Area (m²)
\( RA/V \) — Surface to Volume Ratio (1/m)
\( [Tribonacci_C] \) — Tribonacci constant (1.839286755214161)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the total surface area based on the surface to volume ratio, utilizing the mathematical properties of the snub cube and the Tribonacci constant.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for understanding the geometric properties of snub cubes, material requirements for construction, and various applications in architecture and engineering.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Snub Cube?
A: A snub cube is an Archimedean solid with 38 faces - 6 squares and 32 equilateral triangles.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ - x² - x - 1 = 0, approximately 1.839286755214161.

Q3: What are typical surface to volume ratio values?
A: The surface to volume ratio depends on the size of the snub cube, with smaller cubes having higher ratios.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the snub cube geometry and uses its unique mathematical properties.

Q5: What units should I use?
A: Use consistent units - surface to volume ratio in 1/m will give surface area in m².