Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius Calculator

Formula Used:

\[ TSA = 30 \times \left( \frac{ri \times 2}{\sqrt{\frac{1+0.4715756}{(1-0.4715756) \times (1-2 \times 0.4715756)}}} \right)^2 \times (2+3 \times 0.4715756) \times \frac{\sqrt{1-0.4715756^2}}{1-2 \times 0.4715756^2} \]

Total Surface Area of Pentagonal Hexecontahedron:

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1. What is Total Surface Area of Pentagonal Hexecontahedron?

The Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron. It represents the sum of the areas of all the faces of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( TSA \) — Total Surface Area of Pentagonal Hexecontahedron (m²)
\( ri \) — Insphere Radius of Pentagonal Hexecontahedron (m)
0.4715756 — Constant value specific to pentagonal hexecontahedron geometry

3. Formula Explanation

Details: This formula calculates the total surface area based on the insphere radius, utilizing geometric properties and mathematical constants specific to the pentagonal hexecontahedron shape.

4. Using the Calculator

Tips: Enter the insphere radius value in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Hexecontahedron?
A: A pentagonal hexecontahedron is a complex polyhedron with 60 pentagonal faces, making it one of the Catalan solids.

Q2: What is Insphere Radius?
A: Insphere radius is the radius of the sphere that is contained by the polyhedron such that all faces just touch the sphere.

Q3: Why is there a constant value of 0.4715756 in the formula?
A: This constant represents specific geometric properties and ratios inherent to the pentagonal hexecontahedron structure.

Q4: What units should I use for input?
A: Use meters for the insphere radius input. The result will be in square meters.

Q5: Can this calculator handle very small or very large values?
A: Yes, the calculator can handle a wide range of values as long as they are positive numbers.