Surface To Volume Ratio Of Rhombicosidodecahedron Given Circumsphere Radius Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{3 \times (30 + (5 \times \sqrt{3}) + (3 \times \sqrt{25 + (10 \times \sqrt{5})}))}{(2 \times \text{Circumsphere Radius}) / \sqrt{11 + (4 \times \sqrt{5})} \times (60 + (29 \times \sqrt{5})))} \]

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Rhombicosidodecahedron?

The Surface to Volume Ratio of a Rhombicosidodecahedron is a geometric measurement that compares the total surface area to the volume of this particular polyhedron. It's an important parameter in materials science and geometry for understanding the relationship between surface properties and volumetric characteristics.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

Circumsphere Radius — The radius of the sphere that contains the Rhombicosidodecahedron with all vertices lying on the sphere (in meters)
√ — Square root function

Explanation: This complex formula accounts for the geometric properties of the Rhombicosidodecahedron, incorporating mathematical constants and the circumsphere radius to calculate the surface to volume ratio.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various scientific and engineering applications, including material science, nanotechnology, and geometric analysis. It helps understand how surface properties scale with volume changes.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid for accurate calculation results.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicosidodecahedron?
A: A Rhombicosidodecahedron is an Archimedean solid with 20 regular triangular faces, 30 square faces, and 12 regular pentagonal faces.

Q2: Why is surface to volume ratio important?
A: It's important for understanding how physical and chemical properties change with size, particularly in nanomaterials and biological systems.

Q3: What units are used in this calculation?
A: The circumsphere radius is in meters, and the resulting surface to volume ratio is in meters⁻¹ (per meter).

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric Rhombicosidodecahedron and may not account for real-world imperfections or variations.

Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the Rhombicosidodecahedron geometry.