The formula to calculate the Volume of a Tetrahedron given its total surface area is:
\[ \text{Volume} = \frac{\sqrt{2}}{12} \left(\frac{\text{Total Surface Area}}{\sqrt{3}}\right)^{\frac{3}{2}} \]
The Volume of a Tetrahedron is the total quantity of three-dimensional space enclosed by its surface. The Total Surface Area of a Tetrahedron is the total quantity of plane enclosed by the entire surface of the tetrahedron.
Let's assume the following value:
Using the formula:
\[ \text{Volume} = \frac{\sqrt{2}}{12} \left(\frac{170}{\sqrt{3}}\right)^{\frac{3}{2}} \approx 114.5951 \, \text{cubic meters} \]
The Volume is approximately 114.5951 cubic meters.
| Total Surface Area (square meters) | Volume (cubic meters) |
|---|---|
| 160 | 104.633989560274216 |
| 165 | 109.576828661688339 |
| 170 | 114.595138230865089 |
| 175 | 119.687799877550091 |
| 180 | 124.853743508634523 |