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 re(2): picture of the center by Charlie)

Maybe a better prespective can be gotten from this 3-D picture.  You have to cross your eyes, to look at the left image with your right eye and the right image with your left eye.  It might help to bring a finger or pencil halfway to the screen and focus on that, then observe the cube in 3-D in the background, taking the finger or pencil away.

Posted by Charlie on 2005-03-07 14:15:51