Surface To Volume Ratio Of Tetrakis Hexahedron Given Insphere Radius Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{3}{\text{Insphere Radius}} \]

Surface to Volume Ratio:

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

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Surface to Volume Ratio} = \frac{3}{\text{Insphere Radius}} \]

Where:

Insphere Radius — The radius of the sphere that is contained by the Tetrakis Hexahedron such that all faces just touch the sphere (in meters)

Explanation: This formula provides a direct relationship between the insphere radius and the surface to volume ratio of the Tetrakis Hexahedron.

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 mechanical strength of polyhedral structures.

4. Using the Calculator

Tips: Enter the insphere radius in 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: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can fit inside the polyhedron while touching all its faces.

Q3: Why is surface to volume ratio important?
A: It indicates how much surface area is available relative to the volume, which affects properties like diffusion rates, heat dissipation, and chemical reactivity.

Q4: What are typical values for surface to volume ratio?
A: The values vary depending on the insphere radius. Smaller polyhedra generally have higher surface to volume ratios.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different relationships between surface to volume ratio and insphere radius.