Question

Find the missing dimension of the cone. Round your answer to the nearest tenth.

Volume = 3.6 in.³

Answer 1

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=3.6\\ h=4.2 \end{cases}\implies 3.6=\cfrac{\pi r^2(4.2)}{3}\implies 10.8=4.2\pi r^2 \\\\\\ \cfrac{10.8}{4.2\pi }=r^2\implies \sqrt{\cfrac{10.8}{4.2\pi }}=r\hspace{5em}\stackrel{\textit{diameter = 2r}}{2\sqrt{\cfrac{10.8}{4.2\pi }}} ~~ \approx ~~ \text{\LARGE 1.8}`