You have a 3x3x3 cube. You bore a circular hole, of diameter 1, from the center of the top face to the center of the bottom face. You bore a similar hole from the left face center to the right face center, and another hole from front center to back center. How much material was removed?

(In reply to picture of the center by Charlie)

I can't quite visualize it in my head, but if the picture isn't misleading me, it looks like the hole is the intersection of a sphere with the unit cube, where the sphere's diameter is the length of a diagonal of one side of the cube.  That makes the sphere's volume pi*(sqrt(2)/2)^3, but then you have to subtract off the six "endcaps" of the sphere that stick out of the cube, and I don't have the geometry to figure out their volume :)

Posted by nj on 2005-03-07 07:42:47