Question

Identify the volume of a sphere with surface area 144π m2. Give your answer in terms of π.

Answer 1

$\bf \textit{surface area of a sphere}\\\\ SA = 4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=144\pi \end{cases}\implies 144\pi =4\pi r^2\implies \cfrac{144\pi }{4\pi }=r^2 \\\\\\ 36=r^2\implies \sqrt{36}=r\implies \underline{6}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi (\underline{6})^3}{3}\implies V=288\pi$