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. minute(s)

Explanation:

Step1: Find the radius of the cylinder

The diameter is 1.4 ft, so the radius \( r=\frac{1.4}{2}=0.7 \) ft.

Step2: Calculate the volume of the cylindrical tank

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

Step3: Calculate the time to fill the tank

The rate of filling is 1.9 \( \text{ft}^3 \) per minute. Time \( t=\frac{\text{Volume}}{\text{Rate}}=\frac{6.9237}{1.9}\approx3.644 \)
Round to the nearest minute, we get 4.

Answer:

4