# 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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#### Solution Preview

What the problem asks is to find the area of the border of the set:

{(x,y,z)|x^2+z^2<=k^2 and x^2+y^2<=k^2}.

In order to better understand the set and to know what we have to integrate, we need to fix one of the three planes, with respect to whom we will integrate. Let's fix for instance the plane generated by the x ...

#### Solution Summary

This shows how to find the surface area of the solid that is the intersection of two solid cylinders.

$2.19