Surface to Volume Ratio of Pentagonal Icositetrahedron Given Volume Calculator

Formula Used:

\[ SA:V = \frac{3\sqrt{\frac{22(5[Tribonacci_C]-1)}{(4[Tribonacci_C])-3}}}{\left(V^{\frac{1}{3}}\cdot\left(\frac{2((20[Tribonacci_C])-37)}{11([Tribonacci_C]-4)}\right)^{\frac{1}{6}}\cdot\sqrt{\frac{11([Tribonacci_C]-4)}{2((20[Tribonacci_C])-37)}}\right)} \]

Surface to Volume Ratio (SA:V):

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1. What is Surface to Volume Ratio of Pentagonal Icositetrahedron?

The surface to volume ratio (SA:V) of a Pentagonal Icositetrahedron is a measure of how much surface area the polyhedron has relative to its volume. It's an important geometric property that influences various physical and chemical properties of the shape.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)
\( V \) — Volume of the Pentagonal Icositetrahedron (m³)

Explanation: The formula calculates the surface area to volume ratio based on the volume of the polyhedron and the mathematical constant Tribonacci_C.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. It affects properties like diffusion rates, heat transfer, and chemical reactivity of geometric shapes.

4. Using the Calculator

Tips: Enter the volume of the Pentagonal Icositetrahedron in cubic meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a Catalan solid with 24 pentagonal faces, 60 edges, and 38 vertices.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ - x² - x - 1 = 0, approximately equal to 1.839286755214161.

Q3: Why is surface to volume ratio important?
A: It determines how efficiently a shape can exchange materials or energy with its environment, which is critical in many scientific and engineering applications.

Q4: What units are used in this calculation?
A: Volume is in cubic meters (m³) and the resulting surface to volume ratio is in inverse meters (m⁻¹).

Q5: Can this calculator handle very large or very small volumes?
A: The calculator can handle a wide range of volume values, but extremely large or small values may be limited by floating-point precision.