Volume Of Pentagonal Bipyramid Given Total Surface Area Calculator

Formula Used:

\[ V = \frac{5+\sqrt{5}}{12} \times \left( \sqrt{\frac{2 \times TSA}{5 \times \sqrt{3}}} \right)^3 \]

Volume of Pentagonal Bipyramid:

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1. What is Volume of Pentagonal Bipyramid?

The volume of a pentagonal bipyramid is the total quantity of three-dimensional space enclosed by the surface of the pentagonal bipyramid. It represents the capacity or the amount of space the solid occupies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{5+\sqrt{5}}{12} \times \left( \sqrt{\frac{2 \times TSA}{5 \times \sqrt{3}}} \right)^3 \]

Where:

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

Explanation: This formula calculates the volume of a pentagonal bipyramid based on its total surface area, using geometric relationships between the surface area and volume of the solid.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, manufacturing, and mathematical research. It helps in determining material requirements, capacity planning, and spatial analysis.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding volume in cubic meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a pentagonal bipyramid?
A: A pentagonal bipyramid is a polyhedron formed by two pentagonal pyramids sharing a common pentagonal base. It has 7 vertices, 15 edges, and 10 triangular faces.

Q2: Why is the formula so complex?
A: The formula involves geometric relationships between surface area and volume, requiring square roots and powers to account for the three-dimensional nature of the solid.

Q3: Can this calculator handle different units?
A: The calculator uses square meters for input and cubic meters for output. For other units, convert your measurements to meters first.

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

Q5: Are there limitations to this formula?
A: This formula is specifically designed for regular pentagonal bipyramids where all edges are equal. It may not be accurate for irregular or distorted shapes.