The formula to calculate the insphere radius of an octahedron given its volume is:
\[ r_i = \left(\frac{3V}{\sqrt{2}}\right)^{\frac{1}{3}} \div \sqrt{6} \]
Where:
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 volume of an octahedron is the total quantity of three-dimensional space enclosed by the entire surface of the octahedron.
Let's assume the following value:
Using the formula:
\[ r_i = \left(\frac{3 \cdot 470}{\sqrt{2}}\right)^{\frac{1}{3}} \div \sqrt{6} \approx 4.0784 \, \text{meters} \]
The insphere radius is approximately 4.0784 meters.
| Volume (cubic meters) | Insphere Radius (meters) |
|---|---|
| 450 | 4.0197 |
| 460 | 4.0493 |
| 470 | 4.0784 |
| 480 | 4.1071 |
| 490 | 4.1355 |