Question

an oil tank has to be drained for maintenance. the tank is shaped like a cylinder that is 4.5 ft long with a diameter of 1.6 ft. suppose oil is drained at a rate of 2.5 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.

Explanation:

Step1: Calculate the radius of the cylinder

The diameter $d = 1.6$ ft, so the radius $r=\frac{d}{2}=\frac{1.6}{2}=0.8$ ft.

Step2: Calculate the volume of the cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. Given $h = 4.5$ ft and $\pi = 3.14$, $r = 0.8$ ft. Then $V=3.14\times(0.8)^{2}\times4.5=3.14\times0.64\times4.5 = 9.0432$ $ft^{3}$.

Step3: Calculate the time to empty the tank

The rate of draining is $2.5$ $ft^{3}$ per minute. Let $t$ be the time in minutes. We know that $V = 2.5t$. So $t=\frac{V}{2.5}=\frac{9.0432}{2.5}=3.61728$ minutes.

Step4: Round the result

Rounding $3.61728$ to the nearest minute gives $4$ minutes.

Answer:

$4$