DURING THE FLIGHT, THE PILOT HAD MANAGED HIS FUEL BY SWITCHING TANKS AT ONE TO TWO HOUR INTERVALS. WHILE ARRIVING, HE HAD BEEN USING FUEL FROM HIS RIGHT TANK AND ELECTED TO CONTINUE USING IT. AS HE WAS ALIGNING THE AIRCRAFT WITH THE RUNWAY, HE MADE A SHARP 360 DEGREE TURN TO AVOID ANOTHER AIRCRAFT AND OBTAIN SPACING. AT ABOUT THAT TIME THE ENGINE LOST POWER. HE ELECTED TO LAND ON A HILL, AND DURING THE APPROACH, HE MANEUVERED THE PLANE UNDER POWER LINES. INVESTIGATION REVEALED THAT THE FUEL SELECTOR WAS STILL POSITIONED TO THE RIGHT TANK, WHICH WAS EMPTY. ABOUT 10.25 GALLONS OF FUEL WAS DRAINED FROM THE LEFT MAIN AND HEADER TANKS. WHEN CHECKED, THE RIGHT FUEL GAUGE INDICATED FROM 20 TO 45 LBS, BUT WOULD CHANGE EACH TIME POWER WAS APPLIED, THE OWNER'S MANUAL STATED THAT WHEN THE FUEL BAYS WERE LESS THAN 1/4 FULL, PROLONGED, UNCOORDINATED FLIGHT COULD RESULT IN FUEL STARVATION.