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October 8th, 2017, 02:27 PM   #1
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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} $
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October 8th, 2017, 04:34 PM   #2
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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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