Edge Length of Elongated Pentagonal Bipyramid given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{\frac{5\sqrt{3}}{2} + 5}{\left(\frac{5+\sqrt{5}}{12} + \frac{\sqrt{25+10\sqrt{5}}}{4}\right) \times AV} \]

Edge Length of Elongated Pentagonal Bipyramid:

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1. What is Edge Length of Elongated Pentagonal Bipyramid?

The Edge Length of Elongated Pentagonal Bipyramid is the length of any edge of this specific polyhedron, which is formed by elongating a pentagonal bipyramid by inserting a pentagonal prism between its two halves.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{\frac{5\sqrt{3}}{2} + 5}{\left(\frac{5+\sqrt{5}}{12} + \frac{\sqrt{25+10\sqrt{5}}}{4}\right) \times AV} \]

Where:

\( l_e \) — Edge Length of Elongated Pentagonal Bipyramid (m)
\( AV \) — SA:V of Elongated Pentagonal Bipyramid (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{5} \) — Square root of 5 (approximately 2.236)

Explanation: This formula calculates the edge length based on the surface area to volume ratio of the elongated pentagonal bipyramid.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties of the polyhedron, including its surface area, volume, and other dimensional characteristics in various applications of solid geometry.

4. Using the Calculator

Tips: Enter the surface area to volume ratio (SA:V) in 1/m. 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: An elongated pentagonal bipyramid is a polyhedron formed by inserting a pentagonal prism between the two halves of a pentagonal bipyramid.

Q2: What units should I use for the SA:V ratio?
A: The SA:V ratio should be entered in reciprocal meters (1/m) to maintain dimensional consistency.

Q3: Can this calculator handle very small or very large values?
A: Yes, the calculator can handle a wide range of positive values, though extremely small values may approach computational limits.

Q4: What are typical values for SA:V ratio of this polyhedron?
A: The SA:V ratio depends on the specific dimensions, but generally ranges based on the polyhedron's proportions.

Q5: Is this formula applicable to other polyhedra?
A: No, this specific formula is derived for the elongated pentagonal bipyramid only. Other polyhedra have different geometric relationships.