Calculate Volume Of 3d Model. The volume will be displayed. If you have this you just sum up the volumes of all tetrahedrons.
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But this is not trivial. The trick is to calculate the signed volume of a tetrahedron based on your triangle and topped off at the origin. Enter massprop on the command line.
This is easily done using.
The volume will be displayed. If 3d model volume is an important aspect of your project you could use voxel to represent your models. If you have this you just sum up the volumes of all tetrahedrons. Select the solid object.