Problem 10 (The Pyramid of Oranges)

Here's a fun problem. Take 14 spheres, each one of radius 1, and stack them in the form of a pyramid (like they do in grocery stores when they stack oranges), putting 9 spheres at the base, 4 on top of those, and 1 at the very top as shown in Figure 1.

What portion of the volume of the "covering" pyramid is filled with these spheres ?

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Last modified on Tuesday, January 12, 1999