Mathematics, 25.06.2019 11:00 Prettygirlbuggy
Determine the area of a cone that its volume is 36 cubic inches and the height is 9 inches.
Answers: 1
![\bf \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=36\\ h=9 \end{cases}\implies 36=\cfrac{\pi r^2(9)}{3}\implies 36\cdot \cfrac{3}{9}=\pi r^2 \\\\\\ 12=\pi r^2\implies \cfrac{12}{\pi }=r^2\implies \sqrt{\cfrac{12}{\pi }}=r \\\\[-0.35em] ~\dotfill](/tpl/images/0015/4002/c117b.png)
![\bf \stackrel{\textit{surface area of a cone}}{SA=\pi r\sqrt{r^2+h^2}+\pi r^2}\implies SA=\pi \sqrt{\cfrac{12}{\pi }}\left( \sqrt{\cfrac{12}{\pi }+9^2} \right)+\pi \cdot \cfrac{12}{\pi } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill SA\approx 68.54757~\hfill](/tpl/images/0015/4002/a21e9.png)
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Determine the area of a cone that its volume is 36 cubic inches and the height is 9 inches....
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