Now here's a poser. Take a cube of material with length of each side = 30mm, ie. volume=27mL Drill a 10mm dia hole from the cenre of one face right through the material. Call that the X axis. Now drill two similar holes in the Y and Z axes - again in the centre of the faces so all three holes intersect. Question: What volume of material is left?

Starting with a volume of 27000 mm^3, I obtained an answer for the final volume once you drill the three cylinders of 20978.6142 mm^3. My answer is based on my thinking that the intersection of three cylinders of equal length and diameter is a sphere. That would mean that having subtracted the volume of three such cylinders from the cube, I would need to add back the equivalent of two of these spheres to prevent double dipping. I sure hope you have the answer. Even if I am wrong it was fun to give it a go. hgmjr

Good find Ronh. That at least confirms what I already suspected about the likelihood of an error in my simplification. hgmjr

Good find. I was given this problem many years ago. I established the shape of the common part of the intersection of two holes. Its projection on two axes was a circle and on the third it was a square. I likened if to a football made up of only four panels each shaped like a Zulu's shield. When it came to the third intersection I realised the shape has more facets on it, but my limited spacial capacity prevented me from imagining its true shape. Now I'll try to follow the math.