The formula to calculate the Volume of a Dodecahedron (\(V\)) is:
\[ V = \frac{(15 + (7 \sqrt{5})) \times l_e^3}{4} \]
Where:
The Volume of a Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Dodecahedron.
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.
Let's assume the following value:
Using the formula:
\[ V = \frac{(15 + (7 \sqrt{5})) \times l_e^3}{4} \]
Evaluating:
\[ V = \frac{(15 + (7 \sqrt{5})) \times 10^3}{4} \]
The Volume is 7663.1189 m³.
| Edge Length (m) | Volume (m³) |
|---|---|
| 1 | 7.6631 |
| 2 | 61.3050 |
| 3 | 206.9042 |
| 4 | 490.4396 |
| 5 | 957.8899 |
| 6 | 1,655.2337 |
| 7 | 2,628.4498 |
| 8 | 3,923.5169 |
| 9 | 5,586.4137 |
| 10 | 7,663.1190 |