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Total Surface Area of Pentagonal Trapezohedron given Surface to Volume Ratio Calculator

Formula Used:

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

1/m

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1. What is Total Surface Area of Pentagonal Trapezohedron?

The Total Surface Area of a Pentagonal Trapezohedron is the total quantity of two dimensional space enclosed on the entire surface of this geometric solid. It represents the sum of all the surface areas of its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Explanation: The formula calculates the total surface area based on the given surface to volume ratio, using geometric constants specific to the pentagonal trapezohedron shape.

3. Importance of Surface Area 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 surface to volume ratio (AV) in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Trapezohedron?
A: A pentagonal trapezohedron is a polyhedron with ten faces, each of which is a kite-shaped quadrilateral. It is the dual polyhedron of a pentagonal antiprism.

Q2: What units should I use for the input?
A: The surface to volume ratio should be entered in reciprocal meters (1/m), and the result will be in square meters (m²).

Q3: Can this calculator handle very small or very large values?
A: The calculator can handle a wide range of values, but extremely small values may approach computational limits.

Q4: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the specific dimensions of the pentagonal trapezohedron and can vary significantly.

Q5: Is this formula applicable to all pentagonal trapezohedra?
A: Yes, this formula is derived from the geometric properties of regular pentagonal trapezohedra and applies to all such shapes.

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