Height of Elongated Pentagonal Pyramid given Volume Calculator

Formula Used:

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

Height of Elongated Pentagonal Pyramid:

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1. What is the Height of Elongated Pentagonal Pyramid?

The height of an elongated pentagonal pyramid is the vertical distance from the apex to the base of the pyramid. It is a crucial geometric measurement that helps determine the overall dimensions and properties of this polyhedral shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

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

Where:

\( h \) — Height of Elongated Pentagonal Pyramid (m)
\( V \) — Volume of Elongated Pentagonal Pyramid (m³)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the height based on the given volume, incorporating geometric constants related to the pentagonal pyramid structure.

3. Importance of Height Calculation

Details: Calculating the height is essential for architectural design, geometric analysis, 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 polyhedron formed by attaching a pentagonal pyramid to a pentagonal prism, creating an extended pyramidal structure.

Q2: What units should I use for volume input?
A: The calculator expects volume input in cubic meters (m³). Convert from other units if necessary before calculation.

Q3: Can this formula be used for regular pentagonal pyramids?
A: No, this specific formula is designed for elongated pentagonal pyramids, which have different geometric properties than regular pyramids.

Q4: What is the precision of the calculation?
A: The calculator provides results with up to 6 decimal places for accurate measurement representation.

Q5: Are there any limitations to this calculation?
A: The formula assumes ideal geometric conditions and may not account for material properties or structural deformations in real-world applications.