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October 8th, 2017, 01:27 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 140 Thanks: 2  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: Southern California, USA Posts: 1,488 Thanks: 749 
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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calculating, cylinders, intersecting, volume 
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