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?

I hope this works.  Here's a link to a picture of the central 1x1 volume--the interesting part, the rest being pure cylinders:

picture

 

 

Posted by Charlie on 2005-03-06 16:59:18