Volume of Truncated Cuboctahedron given Circumsphere Radius Calculator

Formula Used:

\[ V = 2 \times (11 + (7 \times \sqrt{2})) \times \left( \frac{2 \times r_c}{\sqrt{13 + (6 \times \sqrt{2})}} \right)^3 \]

Volume of Truncated Cuboctahedron:

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1. What is the Volume of Truncated Cuboctahedron?

The Volume of Truncated Cuboctahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Cuboctahedron. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = 2 \times (11 + (7 \times \sqrt{2})) \times \left( \frac{2 \times r_c}{\sqrt{13 + (6 \times \sqrt{2})}} \right)^3 \]

Where:

\( V \) — Volume of Truncated Cuboctahedron (m³)
\( r_c \) — Circumsphere Radius of Truncated Cuboctahedron (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the volume based on the circumsphere radius, incorporating mathematical constants and geometric relationships specific to the truncated cuboctahedron shape.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for various applications including architectural design, material science, 3D modeling, and mathematical research involving polyhedral structures.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the volume using the mathematical formula.

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 Circumsphere Radius?
A: The circumsphere radius is the radius of the sphere that contains the truncated cuboctahedron such that all vertices lie on the sphere.

Q3: Are there other ways to calculate the volume?
A: Yes, the volume can also be calculated using edge length or other geometric properties, but this calculator specifically uses the circumsphere radius.

Q4: What are typical applications of this calculation?
A: This calculation is used in geometry research, architectural design, computer graphics, and material science applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the given formula, though practical accuracy depends on the precision of the input values.