Surface To Volume Ratio Of Hexakis Octahedron Given Volume Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{543+176\sqrt{2}}}{\sqrt{6(986+607\sqrt{2})}} \times \left( \frac{\sqrt{6(986+607\sqrt{2})}}{28V} \right)^{1/3} \]

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Hexakis Octahedron?

The Surface to Volume Ratio of a Hexakis Octahedron is a geometric property that represents the relationship between the total surface area and the volume of this particular polyhedron. It indicates how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{543+176\sqrt{2}}}{\sqrt{6(986+607\sqrt{2})}} \times \left( \frac{\sqrt{6(986+607\sqrt{2})}}{28V} \right)^{1/3} \]

Where:

\( V \) — Volume of Hexakis Octahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the surface to volume ratio based on the volume of the Hexakis Octahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is an important geometric property that influences various physical and chemical properties of materials and structures, particularly in fields such as materials science, chemistry, and engineering.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 48 faces, 72 edges, and 26 vertices.

Q2: Why is surface to volume ratio important?
A: Surface to volume ratio affects properties like heat transfer, chemical reactivity, and mechanical strength. Higher ratios generally mean more surface area relative to volume.

Q3: What units are used in this calculation?
A: The volume should be in cubic meters (m³), and the resulting surface to volume ratio will be in inverse meters (m⁻¹).

Q4: Can this calculator handle very large or very small volumes?
A: The calculator can handle a wide range of volume values, but extremely large or small values may be limited by floating-point precision.

Q5: Is this formula specific to Hexakis Octahedron?
A: Yes, this formula is specifically derived for calculating the surface to volume ratio of a Hexakis Octahedron based on its volume.