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Find the area cut out of the cylinder $x^2+z^2=1$ by the cylinder $x^2+y^2=1$.

The problem for me apart from visualisation is the symmetry. Since by equating both the equations the conclusion will be $z^2=y^2$.

Since I cann't parametrize by choosing $z=\sqrt{1-x^2}$ in all the quadrants, I would have to parametrize it in the first quadrant itself.

So the limits will be

$0\le z\le y$, $0\le y\le\sqrt{1-x^2}$ and $0\le x \le1$.

Is this alright??

How to visualize the symmetry ??

tattwamasi amrutam
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  • Do you mean find the surface area of the surface produced from the intersection of the two cylinders or did you mean to say find the volume enclosed by the intersection of the two cylinders? – Wintermute Jan 03 '14 at 13:44
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    See Steinmetz solid. A related question can be found here. For more visualizations, see the first four pictures here (two are interactive). – Lucian Jan 03 '14 at 21:22

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