Processing math: 100%

Volume of Tetrahedron given Total Surface Area Calculator

Formula

The formula to calculate the Volume of a Tetrahedron given its total surface area is:

$\text{Volume} = \frac{\sqrt{2}}{12} \left(\frac{\text{Total Surface Area}}{\sqrt{3}}\right)^{\frac{3}{2}}$

Definition

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.

Example Calculation

Let's assume the following value:

Total Surface Area = 170 square meters

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.

Conversion Chart

Total Surface Area (square meters)	Volume (cubic meters)
160	104.633989560274216
165	109.576828661688339
170	114.595138230865089
175	119.687799877550091
180	124.853743508634523