Measurement of in situ-produced 10 Be concentrations at a prehistoric open cast (i.e. aerially exposed) copper mine on Kythnos island, Aegean, Greece, dated to ~ 5 ka, led to overestimated cosmic ray exposure ages. This strongly suggests that the prehistoric mining activity was too shallow to reach nuclide-free levels in the rock. Considering the independently estimated age of the open cast mine, the 10 Be concentrations measured in the sampled rock surface of the mine are further exploited to estimate the thickness of the excavation. The results obtained point at excavation depths no more than a few decimeters, agreeing with independent archaeological evidence.