James P. DildineCI – 499 Fall 2004September 30, 2004Tetrahedral Volume ProblemImagining the following as a cross section of a pyramid made of several other tetrahedral pyramids we have an empty center that we’dlike to find the volume of.The 2-D figure looks misleading so it would behoove us to create a (bad) 3-D model, shown below:First, we notice that the interior “missing” volume looks like an Octahedron. Second, we decide that to find this volume we can take the volume of the entire pyramid and subtract the volumes of the four regular tetrahedral solids, or we could find the volume of an octahedron. Hmmm…It seems much easier to find the volumes of the 4 tetrahedral pyramidsand just subtract the sum of those volumes from the volume of the larger tetrahedron. First taking ONE tetrahedron and finding it’s volume (at first glance) is relatively simple with the following formula:Volume = 1/3 * area of the base * height of the pyramidBut finding these values requires a little manipulationLet’s assume each tetrahedron has a base of 12 cm, a height of 8