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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 solution | Comment 9 of 12 |

The tetrhedron which is formed by the centers of the balls has sides of 2d. We can constuct a right triangle from the center of the top ball to the plane defined by the centers of the balls at the lowest level. This triangle has a hypotenuse of 2d and the length the horizontal side is d; thus the remaining side is d*sqrt(3).  we must then add d to this value to account for the height of plane above the base level and to the top of the ball.  Thus the total height is d*(1+sqrt(3)) or aprox 2.73d. 

  Posted by Lorne Hrynkiw on 2004-08-04 23:11:02
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