Question

A sphere has a volume of approximately 14,137 cubic inches. What is the length of the radius of the sphere, rounded to the nearest whole inch?

Answer 1

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=14137 \end{cases}\implies 14137=\cfrac{4\pi r^3}{3}\implies 42411=4\pi r^3 \\\\\\ \cfrac{42411}{4\pi }=r^3\implies \sqrt[3]{\cfrac{42411}{4\pi }}=r\implies 14.99994\approx r\implies \stackrel{\textit{rounded up}}{15=r}`