# Calculating complex volume

#### pebe

Joined Oct 11, 2004
626
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?

#### hgmjr

Joined Jan 28, 2005
9,027
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

#### Ron H

Joined Apr 14, 2005
7,014

#### hgmjr

Joined Jan 28, 2005
9,027
Good find Ronh. That at least confirms what I already suspected about the likelihood of an error in my simplification.

hgmjr

#### pebe

Joined Oct 11, 2004
626
Originally posted by Ron H@Mar 19 2006, 06:36 AM