The β decay of 192,190 Pb has been studied using the total absorption technique at the ISOLDE (CERN) facility. The β-decay strength deduced from the measurements, combined with QRPA theoretical calculations, allow us to infer that the ground states of the 192,190 Pb isotopes are spherical. These results represent the first application of the shape determination method using the total absorption technique for heavy nuclei and in a region where there is considerable interest in nuclear shapes and shape effects.