An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 5 ft long with a diameter of 1.8 ft . Suppose oil is drained at a rate of 2.1 ft3 per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.

Question

13-06-2017
Mathematics

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An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 5 ft long with a diameter of 1.8 ft . Suppose oil is drained at a rate of 2.1 ft3 per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.

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jdoe0001 jdoe0001 · Answer 1 · 2017-06-13T22:48:52+02:00

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\qquad \begin{cases} r=radius=\frac{diameter}{2}\\ h=height\\ ----------\\ diameter=1.8\\ r=\frac{1.8}{2}=0.9\\ h=5 \end{cases}\implies V=\pi \cdot 0.9^2\cdot 5\\\\ -------------------------------\\\\ \textit{is draining at }\boxed{2.1}\ \frac{ft^3}{min}\textit{ , it has a total of }\boxed{\pi \cdot 0.9^2\cdot 5} \ ft^3 \\\\\\ \textit{it'll take }\cfrac{\pi \cdot 0.9^2\cdot 5}{2.1}\ minutes[/tex]