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?

The integration seems horrendous.  One method might be to take the intersection of two cylinders, and of three, and then use combinatorics (inclusion/exclusion) to get the desired union of three cylinders.

Posted by Charlie on 2005-03-06 17:06:49