The formula to calculate the Insphere Radius of an Octahedron given its total surface area is:
\[ \text{Insphere Radius} = \sqrt{\frac{\text{Total Surface Area}}{2\sqrt{3}}} \div \sqrt{6} \]
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 Total Surface Area of an Octahedron is the total quantity of plane enclosed by the entire surface of the octahedron.
Let's assume the following value:
Using the formula:
\[ \text{Insphere Radius} = \sqrt{\frac{350}{2\sqrt{3}}} \div \sqrt{6} \approx 4.1036 \, \text{meters} \]
The Insphere Radius is approximately 4.1036 meters.
Total Surface Area (square meters) | Insphere Radius (meters) |
---|---|
340 | 4.044534290501121 |
345 | 4.074164974470443 |
350 | 4.103581710087432 |
355 | 4.132789065936760 |
360 | 4.161791450287818 |