Mathematics, 30.08.2019 21:30 daveankatie1671
Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. if the tunnel is initially full, how long will it take for it to be one-third full? what is the height of the water level? assume the radius to be 3 inches and the altitude of the cone to be 4 inches.
Answers: 1
![\bf 12\pi =\cfrac{\pi \cdot 3^2h^2 h}{4^2}\implies 12\pi =\cfrac{9\pi h^3}{16}\implies \cfrac{192\pi }{9\pi }=h^3 \\\\\\ \sqrt[3]{\cfrac{192\pi }{9\pi }}=h\implies \sqrt[3]{\cfrac{64}{3}}=h\implies \cfrac{4}{\sqrt[3]{3}}=h \\\\\\ \cfrac{4}{\sqrt[3]{3}}\cdot \cfrac{\sqrt[3]{3^2}}{\sqrt[3]{3^2}}=h\implies \cfrac{4\sqrt[3]{9}}{\sqrt[3]{3^3}}=h\implies \cfrac{4\sqrt[3]{9}}{3}=h](/tpl/images/0213/0327/fff6d.png)
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Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. i...
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