Surface To Volume Ratio Of Truncated Icosahedron Given Total Surface Area Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12 \times ((10 \times \sqrt{3}) + \sqrt{25 + (10 \times \sqrt{5})})}{\sqrt{\frac{\text{Total Surface Area}}{3 \times ((10 \times \sqrt{3}) + \sqrt{25 + (10 \times \sqrt{5})})}} \times (125 + (43 \times \sqrt{5}))} \]

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Truncated Icosahedron?

The surface to volume ratio of a truncated icosahedron is a geometric property that represents the relationship between the total surface area and the volume of this polyhedron. A truncated icosahedron is an Archimedean solid with 32 faces (12 pentagons and 20 hexagons), 90 edges, and 60 vertices.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

\( \text{Total Surface Area} \) — The total surface area of the truncated icosahedron in square meters
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the ratio of surface area to volume based on the given total surface area of the truncated icosahedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is an important geometric property that finds applications in various fields including materials science, chemistry, and engineering. It helps in understanding properties like heat transfer, diffusion rates, and chemical reactivity of materials with this specific geometric shape.

4. Using the Calculator

Tips: Enter the total surface area of the truncated icosahedron in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated icosahedron?
A: A truncated icosahedron is an Archimedean solid obtained by truncating the vertices of a regular icosahedron. It has 32 faces (12 pentagons and 20 hexagons) and is known for its soccer ball shape.

Q2: What units should I use for the input?
A: The calculator expects the total surface area in square meters (m²). The result will be in reciprocal meters (m⁻¹).

Q3: Can this calculator handle very large or very small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may affect computational precision.

Q4: What are typical applications of this calculation?
A: This calculation is useful in materials science, nanotechnology, and geometric modeling where truncated icosahedron shapes are encountered, such as in fullerenes (buckyballs) and certain crystal structures.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical formulas and should be highly accurate for valid input values. The result is rounded to 6 decimal places for readability.