New Experiments with Spheres-Gas (NEWS-G) is a dark matter direct detection experiment that will operate at SNOLAB (Canada). Similar to other rare-event searches, the materials used in the detector construction are subject to stringent radiopurity requirements. The detector features a 140-cm diameter proportional counter comprising two hemispheres made from commercially sourced 99.99% pure copper. Such copper is widely used in rare-event searches because it is readily available, there are no long-lived Cu radioisotopes, and levels of non-Cu radiocontaminants are generally low. However, measurements performed with a dedicated 210Po alpha counting method using an XIA detector confirmed a problematic concentration of 210Pb in bulk of the copper. To shield the proportional counters active volume, a low-background electroforming method was adapted to the hemispherical shape to grow a 500-$mu$m thick layer of ultra-radiopure copper to the detectors inner surface. In this paper the process is described, which was prototyped at Pacific Northwest National Laboratory (PNNL), USA, and then conducted at full scale in the Laboratoire Souterrain de Modane in France. The radiopurity of the electroplated copper was assessed through Inductively Coupled Plasma Mass Spectrometry (ICP-MS). Measurements of samples from the first (second) hemisphere give 68% confidence upper limits of <0.58 $mu$Bq/kg (<0.24 $mu$Bq/kg) and <0.26 $mu$Bq/kg (<0.11 $mu$Bq/kg) on the 232Th and 238U contamination levels, respectively. These results are comparable to previously reported measurements of electroformed copper produced for other rare-event searches, which were also found to have low concentration of 210Pb consistent with the background goals of the NEWS-G experiment.
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