Question

The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter?

Answer 1

`V=(4)/(3)\pi R^3;\ S_A=4\pi R^2\\------------------\\V=3,000\pi\ m^3\\\\(4)/(3)\pi R^3=3,000\pi\ \ \ |divide\ both\ sides\ by\ \pi\\\\(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)}`


`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)`