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Surface To Volume Ratio Of Tetrakis Hexahedron Given Volume Calculator

Formula Used:

\[ RA/V = \sqrt{5} \times 2 \times \left( \frac{3}{2 \times V} \right)^{1/3} \]

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1. What is Surface to Volume Ratio of Tetrakis Hexahedron?

The Surface to Volume Ratio of Tetrakis Hexahedron is the numerical ratio of the total surface area to the volume of this particular polyhedron. It's an important geometric property that indicates how much surface area is available per unit volume.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ RA/V = \sqrt{5} \times 2 \times \left( \frac{3}{2 \times V} \right)^{1/3} \]

Where:

Explanation: This formula calculates the surface to volume ratio based on the volume of the Tetrakis Hexahedron, using mathematical constants and cube root operations.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. It helps understand properties like heat transfer, chemical reactivity, and structural efficiency of geometric shapes.

4. Using the Calculator

Tips: Enter the volume of the Tetrakis Hexahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that is the dual of the truncated octahedron. It has 24 faces, 36 edges, and 14 vertices.

Q2: Why is the surface to volume ratio important?
A: This ratio helps understand how the shape's surface area relates to its volume, which is important for applications involving heat transfer, diffusion, and material properties.

Q3: What units should I use for volume?
A: The calculator expects volume in cubic meters (m³). If you have volume in other units, convert it to cubic meters first.

Q4: Can this calculator handle very small volumes?
A: Yes, but extremely small volumes may result in very large surface to volume ratios due to the inverse relationship in the formula.

Q5: What are typical values for this ratio?
A: The ratio varies significantly based on the volume. Larger volumes typically have smaller ratios, while smaller volumes have larger ratios.

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