Edge Length of Elongated Pentagonal Pyramid given Volume Calculator

Formula Used:

\[ l_e = \left( \frac{V}{\frac{5+\sqrt{5}}{24} + \frac{\sqrt{25+(10\sqrt{5})}}{4}} \right)^{\frac{1}{3}} \]

Edge Length of Elongated Pentagonal Pyramid:

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1. What is the Edge Length of Elongated Pentagonal Pyramid?

The edge length of an elongated pentagonal pyramid refers to the length of any edge of this geometric solid. It is a fundamental measurement used to describe the size and proportions of the pyramid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \left( \frac{V}{\frac{5+\sqrt{5}}{24} + \frac{\sqrt{25+(10\sqrt{5})}}{4}} \right)^{\frac{1}{3}} \]

Where:

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

Explanation: This formula calculates the edge length based on the given volume of the elongated pentagonal pyramid, using mathematical constants derived from its geometric properties.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from volume is essential for geometric modeling, architectural design, and understanding the spatial properties of elongated pentagonal pyramids in various applications.

4. Using the Calculator

Tips: Enter the volume of the elongated pentagonal pyramid in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated pentagonal pyramid?
A: An elongated pentagonal pyramid is a geometric solid formed by attaching a pentagonal pyramid to a pentagonal prism, creating an elongated structure with pentagonal bases.

Q2: Why is this formula specific to elongated pentagonal pyramids?
A: The formula incorporates mathematical constants derived from the unique geometric properties and proportions of elongated pentagonal pyramids.

Q3: What units should be used for volume input?
A: The calculator expects volume input in cubic meters (m³). For other units, convert to cubic meters first.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the geometric properties of elongated pentagonal pyramids, assuming exact input values.

Q5: Can this calculator be used for other pyramid types?
A: No, this calculator is specifically designed for elongated pentagonal pyramids. Other pyramid types have different geometric formulas.