Question

an oil tank has to be drained for maintenance. the tank is shaped like a cylinder that is 4 ft long with a diameter of 2.4 ft. suppose oil is drained at a rate of 1.5 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: Find the volume of the cylindrical tank

The formula for the volume of a cylinder is \( V = \pi r^2 h \). The diameter is 2.4 ft, so the radius \( r=\frac{2.4}{2}=1.2 \) ft, and the height (length) \( h = 4 \) ft. Using \( \pi = 3.14 \), we have:
\( V=3.14\times(1.2)^2\times4 \)
First, calculate \( (1.2)^2 = 1.44 \). Then, \( 3.14\times1.44 = 4.5216 \). Then, \( 4.5216\times4 = 18.0864 \) cubic feet.

Step2: Calculate the time to empty the tank

The rate of draining is 1.5 \( \text{ft}^3 \) per minute. Time \( t \) is volume divided by rate, so \( t=\frac{V}{\text{rate}}=\frac{18.0864}{1.5} \)
\( \frac{18.0864}{1.5}=12.0576 \)
Round to the nearest minute, we get 12.

Answer:

12