# Find the surface area of the intersection of two cylinders.

Find the surface area of the solid that is the intersection of the two solid cylinders:

x^2 + z^2 <= k^2 (x squared plus z squared is less than or equal to a constant squared) AND

x^2 + y^2 <= k^2 (x squared plus y squared is less than or equal to the same constant squared)

What is my f(x,y)? What are my limits of integration?

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...d y axis. So the way we want to regard our set is as a reunion of segments orthogonal on different points (x,y) that go through the plane. As long as (x,y) satisfies x^2+y^2<=k^2, there are points (x,y,z) that are in our initial set. This points will be those points that satisfy the other equation also, so the points ...