Question

the empty gas tank of a truck needs to be completely filled. the tank is shaped like a cylinder that is 4.5 ft long with a diameter of 1.4 ft. suppose gas is poured into the tank at a rate of 1.9 ft³ per minute. how many minutes does it take to fill the empty 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

Given the diameter \(d = 1.4\) ft, the radius \(r=\frac{d}{2}=\frac{1.4}{2}=0.7\) ft.

Step2: Calculate the volume of the cylindrical tank

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substituting \(r = 0.7\) ft, \(h=4.5\) ft and \(\pi = 3.14\), we get \(V=3.14\times(0.7)^{2}\times4.5\).
First, calculate \((0.7)^{2}=0.49\). Then \(V = 3.14\times0.49\times4.5\).
\(3.14\times0.49 = 1.5386\), and \(1.5386\times4.5=6.9237\) \(ft^{3}\).

Step3: Calculate the time to fill the tank

The rate of pouring gas is \(1.9\) \(ft^{3}\) per minute. Using the formula \(t=\frac{V}{rate}\), where \(V = 6.9237\) \(ft^{3}\) and rate \(=1.9\) \(ft^{3}/\text{min}\).
\(t=\frac{6.9237}{1.9}\approx 3.644\). Rounding to the nearest minute, \(t\approx4\) minutes.

Answer:

\(4\)