Surface to Volume Ratio of Truncated Rhombohedron given Circumsphere Radius Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{(3\sqrt{5+2\sqrt{5}})+(5\sqrt{3})-(2\sqrt{15})}{2 \times \frac{5}{3} \times \sqrt{\sqrt{5}-2}} \times \frac{\sqrt{14-2\sqrt{5}}}{4 \times \text{Circumsphere Radius}} \]

Surface to Volume Ratio of Truncated Rhombohedron:

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

The Surface to Volume Ratio of a Truncated Rhombohedron is the numerical ratio of the total surface area to the volume of this specific polyhedron. It's an important geometric property that describes how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

Circumsphere Radius — The radius of the sphere that contains the Truncated Rhombohedron with all vertices lying on the sphere (in meters)

Explanation: This formula calculates the surface to volume ratio based on the circumsphere radius of the truncated rhombohedron, incorporating various square root terms that come from the geometric properties of this specific 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. For polyhedra like the truncated rhombohedron, this ratio helps understand properties like heat transfer, chemical reactivity, and structural efficiency.

4. Using the Calculator

Tips: Enter the circumsphere radius of the truncated rhombohedron in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated rhombohedron?
A: A truncated rhombohedron is a polyhedron created by truncating the vertices of a rhombohedron, resulting in a shape with both triangular and hexagonal faces.

Q2: What is the circumsphere radius?
A: The circumsphere radius is the radius of the sphere that contains the polyhedron such that all vertices lie on the surface of the sphere.

Q3: Why is surface to volume ratio important?
A: This ratio is important in many scientific applications as it affects properties like diffusion rates, heat dissipation, and chemical reactivity.

Q4: What units are used in this calculation?
A: The circumsphere radius is input in meters (m), and the surface to volume ratio is returned in reciprocal meters (m⁻¹).

Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for truncated rhombohedra. Other polyhedra have different formulas for calculating surface to volume ratios.