The pilot performed a preflight inspection for the cross-country flight, which included checking the fuel tanks. He used a calibrated stick, and determined that he had 15 gallons in the right fuel tank and 10 gallons in the left fuel tank; he flew the majority of the flight with the right fuel tank selected. Upon reaching the destination airport, as he was switching from the right fuel tank position to the BOTH position, the engine surged. As the pilot made a left turn onto base, he noted that the airplane was slightly high so he initiated a left slip to lose altitude. When he leveled the airplane, the engine began to surge as if it were out of fuel. The pilot reported that he tried to maintain engine power by “pumping the throttle but was unable to get any power.” The pilot stated that he was not going to make the runway, so he made a forced landing on a dirt path. The airplane landed hard and the right main landing gear collapsed. The pilot reported that there were no mechanical problems with the airplane. Also, his statement noted that he should have been at the correct airspeed for the approach, which would have made it unnecessary to slip the airplane, and that he should not have slipped the airplane to the left in order to keep fuel available to the engine.