Surface to Volume Ratio of Elongated Dodecahedron Given Width Calculator

Surface to Volume Ratio of Elongated Dodecahedron Formula:

\[ \text{Surface to Volume Ratio} = \frac{\sqrt{3} \times (3 + \sqrt{5})}{\text{Width}} \]

Surface to Volume Ratio:

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Surface to Volume Ratio of an Elongated Dodecahedron is a geometric measurement that compares the total surface area of the shape to its volume. It's an important parameter in materials science and engineering that indicates how much surface area is available per unit volume.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Surface to Volume Ratio} = \frac{\sqrt{3} \times (3 + \sqrt{5})}{\text{Width}} \]

Where:

\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{5} \) — Square root of 5 (approximately 2.236)
Width — The horizontal width measurement of the elongated dodecahedron

Explanation: This formula calculates how much surface area exists relative to the volume of an elongated dodecahedron based on its width dimension.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in many scientific and engineering applications, including heat transfer calculations, chemical reaction rates, material strength analysis, and biological processes where surface interaction is important.

4. Using the Calculator

Tips: Enter the width of the elongated dodecahedron in meters. The value must be positive and greater than zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron with 12 faces that has been stretched along one axis, creating a longer shape than a regular dodecahedron.

Q2: Why is surface to volume ratio important?
A: It's important in many physical and chemical processes. Higher ratios mean more surface area relative to volume, which affects properties like heat dissipation, reaction rates, and strength-to-weight ratios.

Q3: What units are used for this calculation?
A: The width should be in meters, and the resulting surface to volume ratio will be in reciprocal meters (m⁻¹).

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to elongated dodecahedra. Other polyhedra have different formulas for calculating their surface to volume ratios.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect elongated dodecahedra. The accuracy in practical applications depends on how closely the actual object matches the ideal geometric shape.