Volume Of Rhombicuboctahedron Calculator

Rhombicuboctahedron Volume Formula:

\[ V = \frac{2}{3} \times (6 + 5\sqrt{2}) \times l_e^3 \]

Volume of Rhombicuboctahedron:

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1. What is the Rhombicuboctahedron Volume Formula?

The Rhombicuboctahedron volume formula calculates the total three-dimensional space enclosed by the surface of a Rhombicuboctahedron, which is an Archimedean solid with 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the Rhombicuboctahedron volume formula:

\[ V = \frac{2}{3} \times (6 + 5\sqrt{2}) \times l_e^3 \]

Where:

\( V \) — Volume of Rhombicuboctahedron (m³)
\( l_e \) — Edge length of Rhombicuboctahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula combines the mathematical constant √2 with the cube of the edge length to calculate the volume of this specific polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, architecture, and various scientific fields where spatial measurements are required.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 26 faces (8 equilateral triangles and 18 squares), 24 identical vertices, and 48 edges.

Q2: Why does the formula include √2?
A: The square root of 2 appears naturally in the geometry of the Rhombicuboctahedron due to the relationships between its edge lengths and spatial dimensions.

Q3: Can I use different units?
A: Yes, but ensure consistency. If you input edge length in centimeters, the volume will be in cubic centimeters. The calculator defaults to meters.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the input edge length, using the precise formula for Rhombicuboctahedron volume.

Q5: What are practical applications of this calculation?
A: This calculation is used in geometry education, architectural design, 3D modeling, and any field requiring precise volume calculations of polyhedral shapes.