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

Formula Used:

\[ SA:V = \frac{\frac{9}{45}\sqrt{10(157+31\sqrt{5})}}{\sqrt{\frac{370+164\sqrt{5}}{25}}} \times \sqrt{\frac{9\sqrt{10(157+31\sqrt{5})}}{11 \times TSA}} \]

Surface to Volume Ratio (SA:V):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Surface to Volume Ratio (SA:V) of a Deltoidal Hexecontahedron is a geometric property that represents the relationship between the total surface area and the volume of this polyhedron. It is an important parameter in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ SA:V = \frac{\frac{9}{45}\sqrt{10(157+31\sqrt{5})}}{\sqrt{\frac{370+164\sqrt{5}}{25}}} \times \sqrt{\frac{9\sqrt{10(157+31\sqrt{5})}}{11 \times TSA}} \]

Where:

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

Explanation: This formula calculates the surface to volume ratio based on the total surface area of the deltoidal hexecontahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

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 in understanding properties like diffusion rates, heat transfer, and chemical reactivity for geometric structures.

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 Hexecontahedron?
A: A Deltoidal Hexecontahedron is a polyhedron with 60 faces, each of which is a deltoid (kite-shaped quadrilateral). It is a Catalan solid, the dual of the rhombicosidodecahedron.

Q2: What units are used for the surface to volume ratio?
A: The surface to volume ratio is typically expressed in inverse meters (m⁻¹), representing square meters of surface area per cubic meter of volume.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the geometric properties of the deltoidal hexecontahedron, assuming perfect geometric form.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the deltoidal hexecontahedron. Other polyhedra have different surface to volume ratio formulas.

Q5: What are typical values for this ratio?
A: The surface to volume ratio depends on the size of the polyhedron. Smaller polyhedra generally have higher surface to volume ratios than larger ones of the same shape.