The formula to calculate the Insphere Radius of an Octahedron given its surface to volume ratio is:
\[ \text{Insphere Radius} = \frac{3}{\text{Surface to Volume Ratio}} \]
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. The Surface to Volume Ratio of an Octahedron is the numerical ratio of the total surface area to the volume of the octahedron.
Let's assume the following value:
Using the formula:
\[ \text{Insphere Radius} = \frac{3}{0.7} \approx 4.2857 \, \text{meters} \]
The Insphere Radius is approximately 4.2857 meters.
| Surface to Volume Ratio (1 per meter) | Insphere Radius (meters) |
|---|---|
| 0.6 | 5.000000000000000 |
| 0.65 | 4.615384615384615 |
| 0.7 | 4.285714285714286 |
| 0.75 | 4.000000000000000 |