Volume Of Elongated Pentagonal Bipyramid Given Total Surface Area Calculator

Formula Used:

\[ V = \left( \frac{5 + \sqrt{5}}{12} + \frac{\sqrt{25 + 10\sqrt{5}}}{4} \right) \times \left( \sqrt{\frac{SA_{Total}}{\frac{5\sqrt{3}}{2} + 5}} \right)^3 \]

Volume of Elongated Pentagonal Bipyramid:

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1. What is the Volume of Elongated Pentagonal Bipyramid?

The Volume of Elongated Pentagonal Bipyramid is the total quantity of three-dimensional space enclosed by the surface of the Elongated Pentagonal Bipyramid. It represents the capacity of this geometric solid.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ V = \left( \frac{5 + \sqrt{5}}{12} + \frac{\sqrt{25 + 10\sqrt{5}}}{4} \right) \times \left( \sqrt{\frac{SA_{Total}}{\frac{5\sqrt{3}}{2} + 5}} \right)^3 \]

Where:

\( V \) — Volume of Elongated Pentagonal Bipyramid (m³)
\( SA_{Total} \) — Total Surface Area of the bipyramid (m²)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the volume based on the total surface area measurement, using geometric relationships specific to the elongated pentagonal bipyramid shape.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and architecture. It helps in understanding spatial relationships, material requirements, and structural properties of three-dimensional objects.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding volume of the elongated pentagonal bipyramid.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated pentagonal bipyramid?
A: An elongated pentagonal bipyramid is a polyhedron formed by elongating a pentagonal bipyramid by inserting a pentagonal prism between its two halves.

Q2: What units should I use for the input?
A: The calculator expects the total surface area in square meters (m²), and returns the volume in cubic meters (m³).

Q3: Can this calculator handle very large or very small values?
A: Yes, the calculator can process a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision.

Q4: Is this formula accurate for all elongated pentagonal bipyramids?
A: Yes, this formula is mathematically derived and provides exact volume calculation for perfect elongated pentagonal bipyramids.

Q5: What if I get an error or unexpected result?
A: Ensure you've entered a positive number for the total surface area. If problems persist, check that your input is a valid numerical value.