Total Surface Area Of Triakis Octahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ TSA = 6 \times \left( \frac{6 \times \sqrt{23 - 16 \times \sqrt{2}}}{(2 - \sqrt{2}) \times \frac{RA}{V}} \right)^2 \times \sqrt{23 - 16 \times \sqrt{2}} \]

Total Surface Area of Triakis Octahedron (TSA):

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1. What is the Total Surface Area of Triakis Octahedron?

The Total Surface Area of a Triakis Octahedron is the total quantity of plane enclosed on the entire surface of this polyhedron. It's a Catalan solid that can be derived from an octahedron by adding square pyramids on each face.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 6 \times \left( \frac{6 \times \sqrt{23 - 16 \times \sqrt{2}}}{(2 - \sqrt{2}) \times \frac{RA}{V}} \right)^2 \times \sqrt{23 - 16 \times \sqrt{2}} \]

Where:

\( TSA \) — Total Surface Area of Triakis Octahedron (m²)
\( \frac{RA}{V} \) — Surface to Volume Ratio of Triakis Octahedron (1/m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the total surface area based on the given surface to volume ratio, using the geometric properties of the Triakis Octahedron.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material science, architecture, and engineering design where surface properties affect functionality and performance.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that results from adding square pyramids to each face of a regular octahedron.

Q2: What are the units for surface to volume ratio?
A: Surface to volume ratio is measured in 1/m (inverse meters), representing the ratio of surface area to volume.

Q3: Can this calculator handle very small or very large values?
A: The calculator can handle a wide range of values, but extremely small values may approach computational limits.

Q4: What is the significance of the constants in the formula?
A: The constants (23, 16, 6, etc.) are derived from the geometric properties of the Triakis Octahedron and its relationship to the regular octahedron.

Q5: Are there alternative methods to calculate surface area?
A: Yes, surface area can also be calculated from edge length or other geometric parameters, but this calculator specifically uses surface to volume ratio.