How do I remove an exact rectangle from the rounded face of a hollow cylinder object? I have created some cylinders, removed the top and bottom faces from them, and used the solidify modifier on them.

I am trying to remove a section of the outer cylinder by using a cube of the exact size I want to remove. I thought that using the boolean difference modifier would work but it creates a sort of half union effect.

I can achieve a close result by subdividing the cylinder, moving the edges and then removing the faces, but it is not as precise as I was hoping to achieve.

I have provided some pictures of what I am trying to do and what is happening. Is there a better way for me to achieve this?

Thanks.
You can use the boolean / difference no problem. 

It is such a simple shape that it will still be good topology after you apply the modifier. The reason that you get the hollow cube thingey, is that the two shape have exactly the same height. Weird stuff comes from 3D programs that will have to calculate difference between 2 items witch are the same location. If you scale the box on positive Z just a bit, it will work perfectly. 

Usually I don't like boolean because it trashes the topology, but in this case it fits the part!