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Surface to Volume Ratio of Sphenocorona Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{2 + 3\sqrt{3}}{\frac{1}{2}\sqrt{1 + 3\sqrt{\frac{3}{2}}} + \sqrt{13 + 3\sqrt{6}}} \times \text{Edge Length} \]

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1. What is Surface to Volume Ratio of Sphenocorona?

The Surface to Volume Ratio of Sphenocorona is a geometric measurement that represents the relationship between the total surface area and the volume of a Sphenocorona polyhedron. It is an important parameter in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Surface to Volume Ratio} = \frac{2 + 3\sqrt{3}}{\frac{1}{2}\sqrt{1 + 3\sqrt{\frac{3}{2}}} + \sqrt{13 + 3\sqrt{6}}} \times \text{Edge Length} \]

Where:

Explanation: This formula calculates the surface to volume ratio by combining geometric constants with the edge length of the Sphenocorona polyhedron.

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 determine properties like reactivity, heat transfer, and structural efficiency of polyhedral shapes.

4. Using the Calculator

Tips: Enter the edge length of the Sphenocorona in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Sphenocorona?
A: A Sphenocorona is a Johnson solid, specifically J86, which is a polyhedron with 14 faces: 12 equilateral triangles and 2 squares.

Q2: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the edge length. For a Sphenocorona, the ratio increases as the edge length decreases.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Sphenocorona shape with the given edge length.

Q4: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Sphenocorona shape. Other polyhedra have different surface to volume ratio formulas.

Q5: What units does the calculator use?
A: The calculator uses meters for edge length and returns the surface to volume ratio in reciprocal meters (m⁻¹).

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