When does fuel indicator indicate red index? C172
As always, the answer to this question is in the POH. You should always check the specific POH for the aircraft in question but you can usually find one for common aircraft (such as a 172) online. One such example is here.

Under the section on instruments, and specifically "fuel systems"


  Fuel quantity is measured by two float-type fuel quantity transmitters
  (one in each tank) and indicated by two electrically-operated fuel quantity
  indicators on the left side of the instrument panel. An empty tank is
  indicated by a red line and the letter E. When an indicator shows an empty
  tank, approximately 1.5 gallons remain in a standard tank, and 2 gallons
  remain in a long range tank as unusuable fuel. The indicators cannot be
  relied upon for accurate readings during skids, slips, or unusual attitudes. 


I'm pretty sure the "r" variant in your question is the 172 fitted with long range tanks.