The formula to calculate the Surface to Volume Ratio of an Octahedron (\(RA/V\)) is:
\[ RA/V = \frac{3}{r_i} \]
Where:
The Surface to Volume Ratio of an Octahedron is the numerical ratio of the total surface area to the volume of the Octahedron.
The Insphere Radius of an Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.
Let's assume the following value:
Using the formula:
\[ RA/V = \frac{3}{r_i} \]
Evaluating:
\[ RA/V = \frac{3}{4} \]
The Surface to Volume Ratio is 0.75 1/m.
| Insphere Radius (m) | Surface to Volume Ratio (1/m) |
|---|---|
| 1 | 3.0000 |
| 2 | 1.5000 |
| 3 | 1.0000 |
| 4 | 0.7500 |
| 5 | 0.6000 |
| 6 | 0.5000 |
| 7 | 0.4286 |
| 8 | 0.3750 |
| 9 | 0.3333 |
| 10 | 0.3000 |