1. What is the Volume of Elongated Pentagonal Bipyramid?

The Volume of Elongated Pentagonal Bipyramid represents the total quantity of three-dimensional space enclosed by the surface of this geometric solid. It is calculated based on the edge length of the bipyramid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Elongated Pentagonal Bipyramid (m³)
• \( l_e \) — Edge Length of Elongated Pentagonal Bipyramid (m)
• \( \sqrt{} \) — Square root function

Explanation: The formula combines geometric constants related to pentagonal geometry with the cube of the edge length to calculate the volume.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for understanding the spatial properties of this geometric solid, which has applications in crystallography, architecture, and mathematical modeling.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and valid. The calculator will compute the volume based on the mathematical formula.

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.

Q2: What units should I use for the edge length?
A: The calculator uses meters, but you can use any consistent unit as long as you interpret the volume in the corresponding cubic units.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for the edge length with up to 4 decimal places precision.

Q4: What is the geometric significance of the constants in the formula?
A: The constants (5+√5)/12 and √(25+10√5)/4 are derived from the geometric properties of regular pentagons and their three-dimensional extensions.

Q5: Are there practical applications of this calculation?
A: Yes, this calculation is useful in materials science, crystallography, and architectural design where this specific polyhedral form appears.