If the R area is embedded in the class C and you are operating IFR or VFR in the class C with a clearance, then it must be assumed that ATC have conducted the appropriate co-ord for you to transit thr R area (if active). A similar situation I suggest exists if the R area abuts the class C, but with a ongoing clearance (or not) provided by the C controller. If you are IFR in class E then it should be the same. If you are VFR in E or G then you have to facilitate the ongoing cnce yourself. Step 1 in that case is to ask ATC .... ALWAYS. What you do next depend on the answer.