Volume of Elongated Pentagonal Pyramid given Height Calculator

Formula Used:

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

Volume of Elongated Pentagonal Pyramid:

Unit Converter ▲

Unit Converter ▼

From:	To:

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.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the volume based on the height of the elongated pentagonal pyramid, incorporating mathematical constants related to pentagonal geometry.

3. Importance of Volume Calculation

Details: Accurate volume calculation is essential for various applications including architectural design, material estimation, structural analysis, and geometric modeling of complex polyhedra.

4. Using the Calculator

Tips: Enter the height of the elongated pentagonal pyramid in meters. The value must be positive and valid 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 one face of a pentagonal prism.

Q2: What are the units for volume measurement?
A: Volume is measured in cubic meters (m³) in this calculator, but can be converted to other units as needed.

Q3: Can this formula be used for any height value?
A: Yes, the formula is valid for any positive height value, though extremely large values may require special consideration for practical applications.

Q4: What is the geometric significance of the constants in the formula?
A: The constants (5, √5, etc.) relate to the mathematical properties of pentagons and the golden ratio, which is fundamental to pentagonal geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the elongated pentagonal pyramid, limited only by computational precision.