\(The\ formula\ of\ a\ volume\ of\ a\ sphere:V=\frac{4}{3}\pi R^3\\-------------------------\\d=2R\to R=\frac{d}{2}\\\\d=42\ cm\to R=\frac{42}{2}\ cm=21\ cm\\\\therefore\\\\V=\frac{4}{3}\pi\cdot21^3=\frac{4}{3}\pi\cdot9,261=\frac{37,044}{3}\pi=12,348\pi\approx12,348\cdot3.14\\\\=\boxed{38,772.72\ (cm^3)}\)
