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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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re: solution | Comment 10 of 12 |
(In reply to solution by Lorne Hrynkiw)

You write "This triangle has a hypotenuse of 2d and the length the horizontal side is d; thus the remaining side is d*sqrt(3)." But this triangle is a (slanting) face of the tetrahedron with side length 2d, and its height is slanting, too.  We need instead the vertical height of that tetrahedron, which is the slightly smaller value 2d*sqrt(2/3)=(2d/3)*sqrt(6)=1.632993162d. See, e. g.,

  Posted by Richard on 2004-08-05 00:35:59
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