Question

GEOMETRY HELP!! FIND THE VOLUME IN TERMS IF PI !!! EXPLAIN PLEASE!!

Answer 1

$\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=400\pi \end{cases}\implies 400\pi =4\pi r^2\implies \cfrac{400\pi }{4\pi }=r^2 \\\\\\ 100=r^2\implies \sqrt{100}=r\implies \boxed{10=r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~\hspace{7em}V=\cfrac{4\pi \boxed{10}^3}{3}\implies V=\cfrac{4000\pi }{3}$