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.