Suppose you truncate a cube such that this truncation of a vertex takes away 1/8 of the original area from each of 3 square faces and creates a new equilateral triangle. If you did this to all 8 vertices, what would the volume be? (Only use geometric formulas/reasoning for this problem.)

(In reply to Quick question: by Benjamin J. Ladd)

"When you are taking away the 1/8 area of each square face, do you mean from the original cube regardless of what has been taken away, or do you mean 1/8 of the area of the remaining face?  I hope this question makes sense."

I see what you mean, but I don't think that is what the problem is asking.  I think (but I'm not 100%) that it would matter what order you chopped off the corners, so you would get different answers.

Also, Gamer says "this truncation of a vertex takes away 1/8 of the ORIGINAL AREA from each of 3 square faces."

Hope this helps.  Later!

Posted by nikki on 2004-03-11 09:09:04