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 of the Tetrakis Hexahedron to the volume of the Tetrakis Hexahedron. It's an important geometric property that describes how much surface area is available per unit volume.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Tetrakis Hexahedron (m)
• \( \sqrt{10} \) — Square root of 10 (approximately 3.1623)

Explanation: This formula calculates the surface to volume ratio based on the midsphere radius of the Tetrakis Hexahedron, which is the radius of the sphere that touches all edges of the 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 engineering. It helps determine properties like heat transfer efficiency, chemical reactivity, and structural stability of geometric shapes.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids on each face. It has 24 faces, 36 edges, and 14 vertices.

Q2: What does the surface to volume ratio indicate?
A: A higher surface to volume ratio indicates that the shape has more surface area relative to its volume, which can be important for processes involving surface interactions.

Q3: What are typical values for this ratio?
A: The ratio depends on the size of the Tetrakis Hexahedron. For larger shapes, the ratio decreases, while for smaller shapes, the ratio increases.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different formulas for calculating their surface to volume ratios.

Q5: What is the significance of the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron, providing a fundamental geometric measurement of the shape's size.