Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid Calculator

Surface to Volume Ratio Formula:

\[ SA:V = \frac{\frac{(15\sqrt{3})+\sqrt{25+(10\sqrt{5})}}{4}}{\left(\frac{5(\sqrt{5}+1)\sqrt{\frac{10+(2\sqrt{5})}{4}-1}}{3(10-(2\sqrt{5}))}+\frac{5+\sqrt{5}}{24}\right) \times l_e} \]

Surface to Volume Ratio (SA:V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid?

The surface to volume ratio of a gyroelongated pentagonal pyramid is a geometric measurement that compares the total surface area to the volume of this complex polyhedron. It's an important parameter in materials science, chemistry, and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA:V = \frac{\frac{(15\sqrt{3})+\sqrt{25+(10\sqrt{5})}}{4}}{\left(\frac{5(\sqrt{5}+1)\sqrt{\frac{10+(2\sqrt{5})}{4}-1}}{3(10-(2\sqrt{5}))}+\frac{5+\sqrt{5}}{24}\right) \times l_e} \]

Where:

\( l_e \) — Edge length of the gyroelongated pentagonal pyramid
The numerator represents the total surface area
The denominator represents the volume calculation

Explanation: This complex formula accounts for the unique geometry of the gyroelongated pentagonal pyramid, incorporating both pentagonal and triangular faces in its calculation.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is crucial in determining various physical properties including heat transfer efficiency, chemical reactivity, and structural strength. Higher ratios typically indicate better surface interaction properties.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and non-zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

5. Frequently Asked Questions (FAQ)

Q1: What is a gyroelongated pentagonal pyramid?
A: It's a Johnson solid created by attaching a pentagonal antiprism to a pentagonal pyramid, resulting in a complex polyhedron with both pentagonal and triangular faces.

Q2: Why is surface to volume ratio important?
A: It's critical in many scientific fields - higher ratios improve catalytic efficiency, heat dissipation, and biological processes like nutrient absorption.

Q3: What units does the calculator use?
A: The calculator uses meters for edge length and returns surface to volume ratio in reciprocal meters (m⁻¹).

Q4: Can this calculator handle very small values?
A: Yes, the calculator can process edge lengths with precision up to four decimal places, suitable for microscopic applications.

Q5: Are there practical applications for this calculation?
A: Yes, in nanotechnology, materials science, and architectural design where complex geometric structures with optimal surface properties are required.