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Pile of Cannonballs (Posted on 2004-08-03) Difficulty: 3 of 5
If one stacks 10 cannonballs of diameter d in a pile (tetrahedron), what is the height of the pile?

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Solution the height of a tetrahedron | Comment 1 of 12
It would seem to me that if you can find the height of the tetrahedron that is formed by the centers of all the cannonballs, then the rest is easy. The formula for the height of a tetrahedron is h = 1/3 6 x, where x is the side of the tetrahedron. X would be the same as d in this case. So because there are 3 rows of cannonballs (6 on the bottom, 3 in the middle and 1 on top) you would have to multiply the height by 2 then add one diameter. So 2h + d.
  Posted by Danny on 2004-08-03 18:17:28
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