Surface To Volume Ratio Of Elongated Pentagonal Bipyramid Given Volume Calculator

Formula Used:

\[ SA:V = \frac{\frac{5\sqrt{3}}{2} + 5}{\left(\frac{5+\sqrt{5}}{12} + \frac{\sqrt{25+10\sqrt{5}}}{4}\right) \times \left(\frac{V}{\frac{5+\sqrt{5}}{12} + \frac{\sqrt{25+10\sqrt{5}}}{4}}\right)^{\frac{1}{3}}} \]

Surface to Volume Ratio (SA:V):

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1. What is Surface to Volume Ratio of Elongated Pentagonal Bipyramid?

The surface to volume ratio of an elongated pentagonal bipyramid is a geometric property that represents the relationship between the total surface area and the volume of this specific polyhedron. It is an important parameter in materials science and nanotechnology.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( SA:V \) — Surface to Volume Ratio (m⁻¹)
\( V \) — Volume of the elongated pentagonal bipyramid (m³)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the ratio by dividing the total surface area by the volume, with the volume term adjusted by the cube root to maintain dimensional consistency.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various scientific fields, particularly in nanotechnology, catalysis, and materials science, where surface properties significantly influence material behavior and reactivity.

4. Using the Calculator

Tips: Enter the volume of the elongated pentagonal bipyramid in cubic meters. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated pentagonal bipyramid?
A: An elongated pentagonal bipyramid is a polyhedron formed by adding a pentagonal prism between two pentagonal pyramids, creating an elongated bipyramidal structure.

Q2: Why is surface to volume ratio important?
A: Higher surface to volume ratios indicate more surface area relative to volume, which is important for applications involving surface reactions, heat transfer, and catalytic activity.

Q3: What units are used in this calculation?
A: The calculator uses cubic meters for volume and returns the ratio in inverse meters (m⁻¹).

Q4: Can this calculator handle very small volumes?
A: Yes, the calculator can handle volumes at nanoscale levels, making it useful for nanotechnology applications.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given geometric shape, assuming perfect geometry and accurate input values.