Question

A ball has a volume of 128 cubic inches. Find the diameter of the ball.

Answer 1

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ V=128 \end{cases}\implies 128=\cfrac{4\pi r^3}{3}\implies 128(3)=4\pi r^3$

$\bf \cfrac{128(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{128(3)}{4\pi }}=r^3\implies \sqrt[3]{\cfrac{96}{\pi }}=r\implies \sqrt[3]{\cfrac{8\cdot 12}{\pi }}=r \\\\\\ \sqrt[3]{\cfrac{2^3\cdot 12}{\pi }}=r\implies 2\sqrt[3]{\cfrac{12}{\pi }}=r\\\\ -------------------------------\\\\ \textit{and since the diameter is \underline{twice as the radius}}\qquad d=4\sqrt[3]{\cfrac{12}{\pi }}$