Volume of Truncated Cuboctahedron Given Total Surface Area Calculator

Formula Used:

\[ V = 2 \times (11 + (7 \times \sqrt{2})) \times \left( \sqrt{ \frac{TSA}{12 \times (2 + \sqrt{2} + \sqrt{3})} } \right)^3 \]

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 measurement in 3D space analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = 2 \times (11 + (7 \times \sqrt{2})) \times \left( \sqrt{ \frac{TSA}{12 \times (2 + \sqrt{2} + \sqrt{3})} } \right)^3 \]

Where:

\( V \) — Volume of Truncated Cuboctahedron (m³)
\( TSA \) — Total Surface Area of Truncated Cuboctahedron (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the volume based on the total surface area measurement, using the mathematical relationship between surface area and volume for this specific polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is crucial in various fields including architecture, engineering, manufacturing, and mathematical research. It helps in material estimation, space planning, and structural analysis.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding volume in cubic meters.

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: Why is this specific formula used?
A: This formula establishes the mathematical relationship between the total surface area and volume of a Truncated Cuboctahedron, derived from its geometric properties.

Q3: What units should I use for input?
A: The calculator expects input in square meters for surface area and outputs volume in cubic meters. Consistent units are essential for accurate results.

Q4: Can this calculator handle very large or small values?
A: Yes, the calculator can process a wide range of values, but extremely large or small numbers may be limited by computational precision.

Q5: Is this formula applicable to all polyhedrons?
A: No, this specific formula is only valid for Truncated Cuboctahedrons. Different polyhedrons have different volume-surface area relationships.