\(V=\dfrac{4}{3}\pi R^3\\\\V=\dfrac{500\pi}{3}\ in^3;\ R=?\\\\subtitute\\\\\dfrac{4}{3}\pi R^3=\dfrac{500}{3}\pi\ \ \ |divide\ both\ sides\ by\ \pi\\\\\dfrac{4}{3}R^3=\dfrac{500}{3}\ \ \ |multiply\ both\ sides\ by\ 3\\\\4R^3=500\ \ \ \ |divide\ both\ sides\ by\ 4\\\\R^3=125\to R=\sqrt[3]{125}\\\\\boxed{R=5\ (in)}\)
