The formula to calculate the midsphere radius of a cube given its perimeter is:
\[ r_m = \frac{P}{12 \sqrt{2}} \]
Where:
Midsphere radius of a cube is the radius of the sphere for which all the edges of the cube become a tangent line on that sphere.
Perimeter of a cube is the total distance around the edge of the cube.
Let's assume the following value:
Using the formula:
\[ r_m = \frac{120}{12 \sqrt{2}} \approx 7.07106781186547 \, \text{meters} \]
The midsphere radius of the cube is approximately 7.07106781186547 meters.
| Perimeter (m) | Midsphere Radius (m) |
|---|---|
| 100 | 5.892556509888 |
| 120 | 7.071067811865 |
| 140 | 8.249579113843 |
| 160 | 9.428090415821 |
| 180 | 10.606601717798 |
| 200 | 11.785113019776 |