My Math Forum calculating volume of three intersecting cylinders

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 October 8th, 2017, 01:27 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 calculating volume of three intersecting cylinders Three cylinders of radius 1 intersect at right angles at the origin. Find the volume contained inside all three cylinders. Would anyone show me how to use double integral to solve this problem first with the Cartesian coordinate and then with polar coordinate? Answer: $\displaystyle 16 - 8 \sqrt{2}$
 October 8th, 2017, 03:34 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,505 Thanks: 1374 i vaguely remember doing this by taking 8 times the volume of the solid within the first octant. All 8 octants are identical. That volume would seem to then be $2-\sqrt{2}$ see if you can work it that way.

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