[tex]V=\dfrac{4}{3}\pi R^3;\ S_A=4\pi R^2\\------------------\\V=3,000\pi\ m^3\\\\\dfrac{4}{3}\pi R^3=3,000\pi\ \ \ |divide\ both\ sides\ by\ \pi\\\\\dfrac{4}{3}R^3=3,000\ \ \ \ |multiply\ both\ sides\ by\ 3\\\\4R^3=9,000\ \ \ \ |divide\ both\ sides\ by\ 4\\\\R^3=2,250\to R=\sqrt[3]{2,250}\\\\R=\sqrt[3]{125\cdot18}\\\\R=\sqrt[3]{125}\cdot\sqrt[3]{18}\\\\\boxed{R=5\sqrt[3]{18}\ (m)}[/tex]
[tex]S_A=4\pi\cdot(5\sqrt[3]{18})^2=4\pi\cdot5^2\sqrt[3]{18^2}=4\pi\cdot25\sqrt[3]{324}=100\pi\sqrt[3]{27\cdot12}\\\\=100\pi\cdot\sqrt[3]{27}\cdot\sqrt[3]{12}=100\pi\cdot3\cdot\sqrt[3]{12}=300\pi\sqrt[3]{12}\approx2139\ (m^2)[/tex]
