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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?

No Solution Yet Submitted by ThoughtProvoker    
Rating: 3.0000 (2 votes)

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Solution No Subject | Comment 11 of 12 |

I connected the centers of the 4 spheres on the corner of the pile to create a tetrahedron with edge length of 2d (1/2 d from each of the corner spheres, and d from the middle sphere). The height of this tetrahedron can easily be found using the equation Height = EdgeLength*sqrt(2/3) = 2d * sqrt(2/3).

Then you need to add d to that height. Why? Because there is still d of sphere below the base of the 2d tetrahedron, and there is d of sphere above the top sphere in the pile. So the height of the pile is:

2d*sqrt(2/3) +d = d * (2*sqrt(2/3) + 1)

  Posted by nikki on 2004-08-10 09:31:31
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