Question

find the volume of the smallest right circular cylinder that will hold a sphere whose radius is 4 meters. find the volune of the sphere. show all the steps pleases.

Answer 1

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\quad \begin{cases} r=radius\\ ------\\ r=4 \end{cases}\implies V=\cfrac{4\pi 4^3}{3}\implies V=\cfrac{256\pi }{3}\\\\ -------------------------------\\\\ \cfrac{sphere}{cylinder}\qquad \cfrac{2}{3}\impliedby ratio~thus\implies \cfrac{2}{3}=\cfrac{\stackrel{sphere}{v}}{\stackrel{cylinder}{v}} \implies \cfrac{2}{3}=\cfrac{\frac{256\pi }{3}}{v} \\\\\\ v=\cfrac{3\cdot \frac{256\pi }{3}}{2}\implies v=\cfrac{256\pi }{2}\implies v=128\pi$