A classic problem solved by Archimedes before the invention of calculus, concerns two circular cylinders intersecting at right angles.

If each cylinder has a radius of 1 unit, what is the volume of space that is common to the cylinders?

For warm-up, you can figure out the answer - using calculus if you like.

Here's the puzzle of the day:

What is the volume of space that is common to three orthogonally intersecting cylinders of unit radius?

In both problems the axes of the cylinders intersect.

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Guest Message by DevFuse

# Three intersecting cylinders

Started by bonanova, Aug 06 2012 06:54 AM

4 replies to this topic

### #1

Posted 06 August 2012 - 06:54 AM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 06 August 2012 - 01:55 PM

Spoiler for Dust off the old math portion of my brain...

### #4

Posted 12 August 2012 - 03:10 PM

Is the three cylinder problem also doable without using calculus?

### #5

Posted 13 August 2012 - 07:26 AM

Is the three cylinder problem also doable without using calculus?

Well to be fair, Cavalieri's principle was the calculus dodge for the two cylinder calculation.

It's a near cousin to the integral calculus.

The three cylinder problem might succumb in a similar way.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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