Question

Find the surface area of a sphere with a volume of 33.51 cubic inches

Answer 1

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r = radius\\ \cline{1-1} V=33.51 \end{cases}\implies 33.51=\cfrac{4\pi r^3}{3}\implies 100.53 = 4\pi r^3 \\\\\\ \cfrac{100.53}{4\pi }=r^3\implies 7.9999 \approx r^3\implies 8\approx r^3\implies \sqrt[3]{8}\approx r\implies \boxed{2 \approx r} \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad \implies SA\approx4\pi \left( \boxed{2} \right)^2\implies SA\approx16\pi \implies SA\approx 50.27`