Surface to Volume Ratio of Deltoidal Hexecontahedron given Volume Calculator

Formula Used:

\[ SA:V = \frac{\frac{9}{45} \times \sqrt{10 \times (157 + (31 \times \sqrt{5}))}}{\sqrt{\frac{370 + (164 \times \sqrt{5})}{25}}} \times \left( \frac{45 \times \sqrt{\frac{370 + (164 \times \sqrt{5})}{25}}}{11 \times V} \right)^{\frac{1}{3}} \]

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 represents the relationship between its total surface area and its volume. It is a crucial geometric property that indicates how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( V \) — Volume of Deltoidal Hexecontahedron (m³)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the surface to volume ratio based on the given volume 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 important in various fields including materials science, chemistry, and engineering. For polyhedra, it helps understand properties like heat transfer, diffusion rates, and structural efficiency.

4. Using the Calculator

Tips: Enter the volume of the deltoidal hexecontahedron in cubic 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 Catalan solid with 60 faces, each of which is a kite (deltoid). It is the dual polyhedron of the rhombicosidodecahedron.

Q2: What units should I use for volume?
A: The calculator expects volume in cubic meters (m³). If you have measurements in other units, convert them to cubic meters first.

Q3: Can this calculator handle very small or very large volumes?
A: The calculator can handle a wide range of volume values, but extremely small values (close to zero) may result in computational limitations.

Q4: What does the surface to volume ratio tell us about the shape?
A: A higher SA:V ratio indicates that the shape has more surface area relative to its volume, which can be important for processes involving surface interactions.

Q5: Are there any limitations to this calculation?
A: This calculation assumes a perfect geometric shape and uses mathematical approximations. Real-world objects may have slightly different ratios due to manufacturing imperfections.