Question

A right circular cylinder has a height of 15 and a volume of 1318.8 cubic feet.

what is the diameter in feet of the cylinder?

Answer 1

keeping in mind that the diameter is twice as long as the radius, then


`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ V=1318.8\\ h=15 \end{cases}\implies 1318.8=\pi r^2(15)\implies \cfrac{1318.8}{15\pi }=r^2 \\\\\\ \cfrac{87.92}{\pi }=r^2\implies \sqrt{\cfrac{87.92}{\pi }}=r\qquad \qquad \qquad\qquad\stackrel{\textit{so the diameter is}}{2\sqrt{\cfrac{87.92}{\pi }}}`