Question

The surface area of a sphere is about 2,826 square millimeters. What is the volume of a sphere?

Answer 1

`\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=2826 \end{cases} \implies 2826=4\pi r^2 \\\\\\ \cfrac{2826}{4\pi }=r^2\implies \cfrac{1413}{2\pi }=r^2\implies \sqrt{\cfrac{1413}{2\pi }}=r \\\\[-0.35em] ~\dotfill`

`\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\sqrt{(1413)/(2\pi )} \end{cases}\implies V=\cfrac{4\pi }{3}\cdot \left( \sqrt{\cfrac{1413}{2\pi }} \right)^3 \\\\\\ V=\cfrac{4\pi }{3}\cdot \cfrac{4239√(157)}{2\pi √(2\pi )}\implies V=\cfrac{2826√(157)}{√(2\pi )}\implies V\approx 14126.42~mm^3`