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Brain teaser # 1

GeorgeJ 1080 Maple
December 07 2006
0
A few years ago I saw somewhere in a math forum a brain-teaser type problem which I'm about to present. I wasn't able to solve it at the time. I haven't been able to find the original forum, so I don't know whether or not my answer is right. I do know that I could never have attacked the problem without MAPLE. We have a cube of edge a and a drill bit of diameter b. We drill one hole from the center of the front face to the center of the back face, and another from the center of the right face to the center of the left. What is the total volume of material removed? I get (Pi*(b^2)*a)/2 - ((2/3)*b^3) Am I right? I don't remember whether or not the original problem included this addition: We drill an additional hole from the center of the top of the cube to the center of the bottom. *Now* what is the total amount of material removed from the cube by drilling? I get (3/4)*Pi*(b^2)*a - ((b^3)*sqrt(2)) Am I right?

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