Surface to Volume Ratio of Rhombicosidodecahedron given Midsphere Radius Calculator

Formula Used:

\[ RA/V = \frac{3 \times (30 + (5 \times \sqrt{3}) + (3 \times \sqrt{25 + (10 \times \sqrt{5})}))}{(2 \times r_m) / \sqrt{10 + (4 \times \sqrt{5})} \times (60 + (29 \times \sqrt{5}))} \]

Surface to Volume Ratio of Rhombicosidodecahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Rhombicosidodecahedron?

The Surface to Volume Ratio of a Rhombicosidodecahedron is a geometric property that represents the relationship between the total surface area and the volume of this Archimedean solid. It's an important parameter in materials science and physics for understanding surface properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ RA/V = \frac{3 \times (30 + (5 \times \sqrt{3}) + (3 \times \sqrt{25 + (10 \times \sqrt{5})}))}{(2 \times r_m) / \sqrt{10 + (4 \times \sqrt{5})} \times (60 + (29 \times \sqrt{5}))} \]

Where:

\( RA/V \) — Surface to Volume Ratio (m⁻¹)
\( r_m \) — Midsphere Radius (m)
\( \sqrt{3} \) — Square root of 3 (≈1.732)
\( \sqrt{5} \) — Square root of 5 (≈2.236)

Explanation: This formula calculates the surface area to volume ratio based on the midsphere radius of the rhombicosidodecahedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in materials science for understanding properties like reactivity, heat transfer, and strength-to-weight ratios. For complex polyhedra like the rhombicosidodecahedron, this ratio helps in studying their geometric properties.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding surface to volume ratio.

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: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Why is surface to volume ratio important?
A: It indicates how much surface area is available per unit volume, which affects properties like chemical reactivity and heat dissipation.

Q4: What units are used in this calculation?
A: The midsphere radius is in meters (m), and the surface to volume ratio is in reciprocal meters (m⁻¹).

Q5: Can this calculator handle very small or large values?
A: Yes, as long as the input values are positive numbers, the calculator can handle a wide range of values.