Surface To Volume Ratio Of Deltoidal Icositetrahedron Given Total Surface Area Calculator

Formula Used:

\[ SA:V = \frac{6\sqrt{61+38\sqrt{2}}}{\sqrt{292+206\sqrt{2}}} \times \sqrt{\frac{12\sqrt{61+38\sqrt{2}}}{7 \times TSA}} \]

Surface to Volume Ratio (SA:V):

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

The Surface to Volume Ratio (SA:V) of a Deltoidal 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 characteristics of the shape.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ SA:V = \frac{6\sqrt{61+38\sqrt{2}}}{\sqrt{292+206\sqrt{2}}} \times \sqrt{\frac{12\sqrt{61+38\sqrt{2}}}{7 \times TSA}} \]

Where:

\( TSA \) — Total Surface Area of the Deltoidal Icositetrahedron (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the surface to volume ratio based on the total surface area of the deltoidal icositetrahedron, incorporating the mathematical constants specific to this polyhedron's geometry.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various applications including material science, chemistry, and physics. It affects properties like heat transfer, reaction rates, and structural strength in geometric shapes.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces. It is the dual polyhedron of the rhombicuboctahedron.

Q2: What units should I use for the input?
A: The calculator expects the total surface area in square meters (m²). The result will be in reciprocal meters (m⁻¹).

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

Q4: What does a higher surface to volume ratio indicate?
A: A higher SA:V ratio indicates that the shape has more surface area relative to its volume, which can be important for applications requiring high surface exposure.

Q5: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric shape and uses the mathematical formula specific to the deltoidal icositetrahedron's properties.