Surface To Volume Ratio Of Truncated Dodecahedron Given Dodecahedral Edge Length Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12 \times (\sqrt{3} + 6 \times \sqrt{5 + 2 \times \sqrt{5}})}{l_e \times \frac{1}{\sqrt{5}} \times (99 + 47 \times \sqrt{5})} \]

Surface to Volume Ratio:

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Surface to Volume Ratio of a Truncated Dodecahedron is a geometric property that represents the relationship between the total surface area and the volume of this polyhedron. It is an important parameter in materials science and engineering applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Surface to Volume Ratio} = \frac{12 \times (\sqrt{3} + 6 \times \sqrt{5 + 2 \times \sqrt{5}})}{l_e \times \frac{1}{\sqrt{5}} \times (99 + 47 \times \sqrt{5})} \]

Where:

\( l_e \) — Dodecahedral Edge Length (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{5} \) — Square root of 5 (approximately 2.236)

Explanation: This formula calculates the ratio of surface area to volume for a truncated dodecahedron based on its dodecahedral edge length.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. It affects properties like heat transfer, reaction rates, and structural efficiency.

4. Using the Calculator

Tips: Enter the dodecahedral edge length in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated dodecahedron?
A: A truncated dodecahedron is an Archimedean solid created by cutting the corners of a regular dodecahedron, resulting in 20 regular triangular faces and 12 regular decagonal faces.

Q2: Why is surface to volume ratio important?
A: This ratio indicates how much surface area is available per unit volume, which is critical for processes involving surface interactions like catalysis, heat transfer, and diffusion.

Q3: What units are used in this calculation?
A: The input is in meters (m) and the output is in reciprocal meters (m⁻¹), representing the surface to volume ratio.

Q4: Can this calculator handle very small or very large values?
A: Yes, the calculator can handle a wide range of values, but extremely small values may approach computational limits.

Q5: Are there practical applications for this calculation?
A: Yes, this calculation is used in materials design, nanotechnology, pharmaceutical research, and various engineering applications where geometric properties affect performance.