Surface To Volume Ratio Of Elongated Pentagonal Bipyramid Given Total Surface Area Calculator

Formula Used:

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

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 (SA:V) of an Elongated Pentagonal Bipyramid is a geometric property that represents the ratio of the total surface area to the volume of this polyhedron. It's an important parameter in materials science and nanotechnology.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( TSA \) — Total Surface Area of the elongated pentagonal bipyramid (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the surface to volume ratio based on the total surface area, using the geometric properties specific to the elongated pentagonal bipyramid shape.

3. Importance of Surface to Volume Ratio

Details: The SA:V ratio is crucial in various scientific fields. Higher ratios indicate more surface area relative to volume, which is important in catalysis, heat transfer, and biological systems where surface interactions dominate.

4. Using the Calculator

Tips: Enter the total surface area 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 pentagonal bipyramid?
A: It's a polyhedron formed by attaching two pentagonal pyramids to opposite faces of a pentagonal prism, creating a symmetrical bipyramidal structure.

Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available per unit volume, which affects properties like reactivity, strength, and thermal characteristics.

Q3: What units does this calculator use?
A: The calculator uses square meters for surface area and returns the ratio in meters⁻¹ (per meter).

Q4: Can this calculator handle very large or small values?
A: Yes, but extremely large or small values may be limited by floating-point precision in the calculation.

Q5: Is this formula specific to elongated pentagonal bipyramids?
A: Yes, this formula is specifically derived for the geometric properties of elongated pentagonal bipyramids and may not apply to other shapes.