Total Surface Area Of Elongated Pentagonal Bipyramid Given Volume Calculator

Formula Used:

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

Total Surface Area (TSA):

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1. What is the Total Surface Area of Elongated Pentagonal Bipyramid?

The Total Surface Area (TSA) of an Elongated Pentagonal Bipyramid is the sum of the areas of all its faces. It represents the total two-dimensional space covered by the surface of this three-dimensional geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

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

3. Importance of TSA Calculation

Details: Calculating the total surface area is important for various applications including material estimation, heat transfer calculations, and understanding the geometric properties of this complex polyhedron.

4. Using the Calculator

Tips: Enter the volume of the elongated pentagonal bipyramid 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 bipyramid?
A: An elongated pentagonal bipyramid is a polyhedron formed by adding a pentagonal prism between two pentagonal pyramids, creating an elongated bipyramidal structure.

Q2: Why is the formula so complex?
A: The complexity arises from the geometric relationships between volume and surface area in this specific polyhedral shape, involving multiple faces with different geometries.

Q3: Can this calculator handle different units?
A: The calculator uses cubic meters for volume and square meters for surface area. For other units, convert your values to these standard units before calculation.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in crystallography, architecture, and materials science where such geometric shapes may occur or be designed.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the geometric formula, though rounding may occur in the final displayed result.