Volume of Elongated Pentagonal Pyramid Calculator

Volume of Elongated Pentagonal Pyramid Formula:

\[ V = \left( \frac{5+\sqrt{5}}{24} + \frac{\sqrt{25+(10\sqrt{5})}}{4} \right) \times l_e^3 \]

Volume of Elongated Pentagonal Pyramid:

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1. What is the Volume of Elongated Pentagonal Pyramid?

The Volume of Elongated Pentagonal Pyramid represents the total three-dimensional space enclosed by the surface of this geometric solid. It combines a pentagonal pyramid with a pentagonal prism to form an elongated structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ V = \left( \frac{5+\sqrt{5}}{24} + \frac{\sqrt{25+(10\sqrt{5})}}{4} \right) \times l_e^3 \]

Where:

\( V \) — Volume of Elongated Pentagonal Pyramid (m³)
\( l_e \) — Edge Length of Elongated Pentagonal Pyramid (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula combines the volume contributions from both the pentagonal pyramid and pentagonal prism components of the elongated pyramid structure.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in various fields including architecture, engineering, manufacturing, and mathematical research. It helps in material estimation, structural analysis, and spatial planning.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is an Elongated Pentagonal Pyramid?
A: An elongated pentagonal pyramid is a Johnson solid formed by attaching a pentagonal pyramid to one face of a pentagonal prism.

Q2: What units should I use for the edge length?
A: The calculator uses meters, but you can use any consistent unit of length as the volume will scale with the cube of the length unit.

Q3: Can this formula be used for irregular pyramids?
A: No, this specific formula applies only to regular elongated pentagonal pyramids where all edges are equal.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications.

Q5: Are there real-world applications for this calculation?
A: Yes, this calculation is useful in architectural design, crystal structure analysis, and various engineering applications involving polyhedral structures.