Image to have six pyramides with a side length of A for the base and the height A (see picture below).
Now take these six pyramides and put them together so that the bases form a cube. The top of each pyramide points inward (the top of each pyramide ends in the center of the base of the opposite prymide).
Finally move these pyramides without changing the orientation so that the centers of gravity of all six pyramides will meet at the same point.
Now imagine that all areas of all pyramides are used as a knife to devide the so arranged pyramides into separated volumes. How many volumes will be generated then?
Correct answer: 193
Explanation:
After arranging the pyramides you will have the arrangement shown in fig. 1. The center of gravity is A/4 above the base.
Fig. 1: Pyramide arrangement
Fig. 2 and 3 show the sections on the surface of a single pyramide (two different views).
Fig. 2/3: Sections on the surface of a single pyramide
Fig. 4 shows the volumes of one pyramide. There are 75 volumens which belong to one pyramide. Note, that some of the volumes belong to more than one pyramide. The cubical core is the only part which belongs to all six pyramides.
