1. What Is The Volume Of Truncated Cuboctahedron Given Midsphere Radius?

The volume of a truncated cuboctahedron given its midsphere radius represents the total three-dimensional space enclosed by the surface of this Archimedean solid, calculated using the known midsphere radius.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of the truncated cuboctahedron (m³)
• \( r_m \) — Midsphere radius (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula derives from the geometric properties of the truncated cuboctahedron, relating its volume to the midsphere radius through mathematical constants and relationships.

3. Importance Of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and architecture for determining capacity, material requirements, and structural properties.

4. Using The Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding volume of the truncated cuboctahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cuboctahedron?
A: A truncated cuboctahedron is an Archimedean solid with 26 faces: 12 squares, 8 regular hexagons, and 6 regular octagons.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the truncated cuboctahedron. Other polyhedra have different volume formulas.

Q4: What are the practical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, and mathematical research involving polyhedral structures.

Q5: How accurate is the calculated volume?
A: The calculation is mathematically exact based on the input radius, though practical measurements may introduce some error.