Question

The volume of a fear is 4,000pi m³. What is the surface area of the sphere to the nearest square meter?

Answer 1

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \begin{cases} r=radius\\ -----\\ V=4000\pi \end{cases}\implies 4000\pi =\cfrac{4\pi r^3}{3} \\\\\\ \cfrac{3}{4\pi }\cdot 4000\pi =r^3\implies \boxed{\sqrt[3]{\cfrac{3000}{\pi }}=r}\\\\ -----------------------------\\\\ \textit{surface area of a sphere}\\\\ S=4\pi r^2\qquad \qquad S=4\pi \left( \boxed{\sqrt[3]{\cfrac{3000}{\pi }}} \right)^2\implies S=4\pi \sqrt[3]{\cfrac{9000}{\pi^2}}$