Surface to Volume Ratio of Elongated Dodecahedron given Total Surface Area Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{3 \cdot \sqrt{\frac{\text{Total Surface Area}}{2 \cdot \sqrt{3} \cdot (3 + \sqrt{5})}}} \]

Surface to Volume Ratio:

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

The Surface to Volume Ratio of an Elongated Dodecahedron is a geometric property that represents the relationship between the total surface area and the volume of this particular polyhedron. It's an important parameter in various scientific and engineering applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Surface to Volume Ratio} = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{3 \cdot \sqrt{\frac{\text{Total Surface Area}}{2 \cdot \sqrt{3} \cdot (3 + \sqrt{5})}}} \]

Where:

\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{5} \) — Square root of 5 (approximately 2.236)
Total Surface Area — The total surface area of the elongated dodecahedron in square meters

Explanation: This formula calculates the surface to volume ratio based on the total surface area of the elongated dodecahedron, using mathematical constants and geometric relationships specific to this polyhedron.

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 helps determine properties like heat transfer efficiency, reaction rates, and structural characteristics of three-dimensional objects.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron formed by elongating a regular dodecahedron along one of its axes, creating a shape with 12 pentagonal faces and additional rectangular faces.

Q2: Why is surface to volume ratio important?
A: Surface to volume ratio affects many physical and chemical properties including heat dissipation, reaction rates, and structural efficiency in various applications.

Q3: What units should I use for the calculation?
A: Use consistent units - typically square meters for surface area, which will give results in reciprocal meters (m⁻¹) for the surface to volume ratio.

Q4: 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 be limited by computational precision.

Q5: Is this formula specific to elongated dodecahedrons?
A: Yes, this formula is specifically derived for calculating the surface to volume ratio of elongated dodecahedrons based on their total surface area.