A solid whose plan view and front and side elevations resembled a multiplication symbol (x) bounded by a circle may be viewed here.

It is the third on that page.

The object can be created by imposing 3 cylinders on a cube in each of the x, y and z dimensions.

If the edges of the cube are of unit length, What is the volume of this object?

How mundane (as being simple) a solution can we get?

Great problem, Brian, and interesting link, Richard. Very peculiar indeed that the number pi does not show up in the solution. I wonder if there is an easy way to understand why it doesn't show. Is there maybe an elementary way to calculate the volume, i.e. without using analysis?

Posted by JLo on 2006-11-05 13:08:06