Mathematics, 09.11.2020 17:00, kenna1323
Find the dimensions of a cylinder of volume 17 m3 of minimal cost if the top and bottom are made of material that costs twice as much as the material for the side.
Answers: 2
![\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2} =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m](/tpl/images/0880/2260/dd3e8.png)
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