Volume of Rhombicuboctahedron given Circumsphere Radius Calculator

Volume of Rhombicuboctahedron Formula:

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

Volume of Rhombicuboctahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Rhombicuboctahedron?

The volume of a Rhombicuboctahedron is the total quantity of three dimensional space enclosed by the surface of this Archimedean solid. It's a polyhedron with 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the volume based on the circumsphere radius, which is the radius of the sphere that contains all vertices of the polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in material estimation, structural analysis, and spatial planning.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and non-zero. 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 triangular and 18 square faces, 24 identical vertices, and 48 edges.

Q2: What is the circumsphere radius?
A: The circumsphere radius is the radius of the sphere that passes through all vertices of the polyhedron.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical operations and provides results with 6 decimal places for accuracy.

Q5: What are practical applications of this calculation?
A: This calculation is useful in architectural design, 3D modeling, material science, and geometric analysis where Rhombicuboctahedron shapes are encountered.