[tex]R-the\ radius\ of\ the\ sphere\\\\the\ volume\ of\ the\ sphere:V=\frac{4}{3}\pi R^3\\the\ diameter=2R\ therefore\ R=42:2=21\ (cm)\\\\V=\frac{4}{3}\pi\cdot21^3=\frac{4}{3}\pi\cdot9,261=4\cdot3,087\pi=12,348\pi\\\\=12,348\cdot3.14\approx\boxed{38,772.72\ (cm^3)}[/tex]
