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Volume Of Elongated Pentagonal Bipyramid Given Surface To Volume Ratio Calculator

Formula Used:

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

1/m

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1. What is Volume of Elongated Pentagonal Bipyramid?

The Volume of Elongated Pentagonal Bipyramid is the total quantity of three-dimensional space enclosed by the surface of the Elongated Pentagonal Bipyramid. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for geometric analysis, material estimation, and structural design applications involving elongated pentagonal bipyramids.

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.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated pentagonal bipyramid?
A: An elongated pentagonal bipyramid is a polyhedron formed by attaching two pentagonal pyramids to opposite faces of a pentagonal prism.

Q2: What units should I use for the input?
A: The surface area to volume ratio should be entered in reciprocal meters (1/m).

Q3: What is the typical range of values for SA:V ratio?
A: The SA:V ratio depends on the specific dimensions of the bipyramid, but it should always be a positive value.

Q4: Can this calculator handle very small or very large values?
A: The calculator can handle a wide range of positive values, but extremely small values may approach computational limits.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical formulas and provides results rounded to 4 decimal places for practical use.

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