The formula to calculate the Edge Length of Dodecahedron given Volume is:
\[ l_e = \left( \frac{4V}{15 + 7\sqrt{5}} \right)^{\frac{1}{3}} \]
The Edge Length of a Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron. The Volume of a Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Dodecahedron.
Let's assume the following values:
Using the formula:
\[ l_e = \left( \frac{4 \cdot 7700}{15 + 7\sqrt{5}} \right)^{\frac{1}{3}} = 10.0160169900652 \]
The Edge Length of the Dodecahedron is 10.0160169900652 meters.
| Volume (cubic meters) | Edge Length (meters) |
|---|---|
| 7500 | 9.928536390977992 |
| 7550 | 9.950550956159564 |
| 7600 | 9.972468540091844 |
| 7650 | 9.994290203852451 |
| 7700 | 10.016016990065159 |
| 7750 | 10.037649923338334 |
| 7800 | 10.059190010690196 |
| 7850 | 10.080638241961397 |
| 7900 | 10.101995590215349 |