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ElenaW [278]
3 years ago
7

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.
Mathematics
1 answer:
dangina [55]2 years ago
3 0
\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
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Since there is only 1 digit repeating, let's multiply everything by 10. So:

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Now, subtract n from both sides:

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3.1111...-0.31111...=9n

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And we're done!

Use a calculator to check:

14/45\stackrel{\checkmark}{=}0.31111...

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