Accepted Solutions
Since a rectangle can't be the "midpoint" by definition, you must mean placing a rectangle with equal offsets from all 4 edges.
Relations is the best way to achieve this. You can set the value for the extrude distance and the minor and major diameters of the source cylinder. Or a combination of the two. With a cylinder extruded equally in both directions, you already have a midpoint along the length as well.
There is simply too many ways to do this to come to consensus on the -best- way. If you revolve the initial surface, you can place 4 points in the original sketch to drive the next sketch. Pick your poison 
If you add a datum point to your sketch, you would have a mid-point... literally, if you do what Dale suggested.
But the easy way would be to create a sketch with two circles and a datum point. make a subsequent sketch and size the circle to the point from the previous sketch. You can constrain the datum point in the 1st sketch to that it changes anytime you change the cylinder parameter. You can create relations to manage the height. Next, extrude the 1st sketch as surfaces with capped ends (option) and create the second surface with the second sketch. Now, no matter what you do, you will get a surface between the other surfaces.
Okay, that might be too simplistic (datum points in sketches will become axes or points that are always accessible. This is the easy way to pass a location on from one sketch to the other, from within a feature or as a separate feature.
Since a rectangle can't be the "midpoint" by definition, you must mean placing a rectangle with equal offsets from all 4 edges.
Relations is the best way to achieve this. You can set the value for the extrude distance and the minor and major diameters of the source cylinder. Or a combination of the two. With a cylinder extruded equally in both directions, you already have a midpoint along the length as well.
There is simply too many ways to do this to come to consensus on the -best- way. If you revolve the initial surface, you can place 4 points in the original sketch to drive the next sketch. Pick your poison
