Question

the empty gas tank of a truck needs to be completely filled. the tank is shaped like a cylinder that is 3.5 ft long with a diameter of 1.6 ft. suppose gas is poured into the tank at a rate of 2.3 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: Calculate radius

Radius $r = \frac{diameter}{2} = \frac{1.6}{2} = 0.8$ ft

Step2: Compute cylinder volume

Volume $V = \pi r^2 h = 3.14 \times (0.8)^2 \times 3.5$
$V = 3.14 \times 0.64 \times 3.5 ≈ 7.03$ ft³

Step3: Find time to fill

Time $t = \frac{Volume}{Rate} = \frac{7.03}{2.3} ≈ 3$ minutes

Answer:

3 minutes