Surface to Volume Ratio of Truncated Icosidodecahedron given Volume Calculator

Formula Used:

\[ SA:V = \frac{6 \times (1 + \sqrt{3} + \sqrt{5 + (2 \times \sqrt{5})})}{\left( \frac{V}{5 \times (19 + (10 \times \sqrt{5}))} \right)^{\frac{1}{3}} \times (19 + (10 \times \sqrt{5}))} \]

Surface to Volume Ratio (SA:V):

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1. What is Surface to Volume Ratio of Truncated Icosidodecahedron?

The Surface to Volume Ratio (SA:V) of a Truncated Icosidodecahedron is the numerical ratio of its total surface area to its volume. It is an important geometric property that describes how much surface area the polyhedron has relative to its volume.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA:V = \frac{6 \times (1 + \sqrt{3} + \sqrt{5 + (2 \times \sqrt{5})})}{\left( \frac{V}{5 \times (19 + (10 \times \sqrt{5}))} \right)^{\frac{1}{3}} \times (19 + (10 \times \sqrt{5}))} \]

Where:

\( V \) — Volume of the Truncated Icosidodecahedron (m³)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the surface to volume ratio based on the volume of the truncated icosidodecahedron, using mathematical constants and operations.

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 helps understand properties like reactivity, heat transfer, and diffusion rates in geometric structures.

4. Using the Calculator

Tips: Enter the volume of the truncated icosidodecahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Truncated Icosidodecahedron?
A: A truncated icosidodecahedron is an Archimedean solid with 62 faces: 30 squares, 20 regular hexagons, and 12 regular decagons.

Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available per unit volume, which affects properties like chemical reactivity and heat dissipation.

Q3: What units are used in this calculation?
A: Volume is in cubic meters (m³) and the resulting ratio is in inverse meters (m⁻¹).

Q4: Can this calculator handle very large or small volumes?
A: Yes, as long as the volume is a positive number greater than zero, the calculator can handle a wide range of values.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical operations and provides results with high accuracy, rounded to 12 decimal places.