The formula to calculate the Insphere Radius of a Tetrahedron given its face area is:
\[ \text{Insphere Radius} = \frac{\sqrt{\left(\frac{4 \cdot \text{Face Area}}{\sqrt{3}}\right)}}{2 \cdot \sqrt{6}} \]
The Insphere Radius of a Tetrahedron is the radius of the sphere that is contained by the tetrahedron in such a way that all the faces just touch the sphere. The face area of a tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the tetrahedron.
Let's assume the following value:
Using the formula:
\[ \text{Insphere Radius} = \frac{\sqrt{\left(\frac{4 \cdot 45}{\sqrt{3}}\right)}}{2 \cdot \sqrt{6}} \approx 2.0809 \, \text{meters} \]
The Insphere Radius is approximately 2.0809 meters.
| Face Area (square meters) | Insphere Radius (meters) |
|---|---|
| 40 | 1.961887304255141 |
| 42 | 2.010336261506363 |
| 44 | 2.057644763815479 |
| 46 | 2.103889746110079 |
| 48 | 2.149139863647084 |
| 50 | 2.193456688254154 |