Question

word problem involving the rate of filling or emptying a cylinder
the empty gas tank of a truck needs to be completely filled. the tank is shaped like a cylinder that is 5 ft long with a diameter of 1.4 ft. suppose gas is poured into the tank at a rate of 1.7 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 radius of cylinder

Radius $r = \frac{1.4}{2} = 0.7$ ft

Step2: Compute volume of cylinder

Volume $V = \pi r^2 h = 3.14 \times (0.7)^2 \times 5$
$V = 3.14 \times 0.49 \times 5 = 7.693$ ft³

Step3: Find time to fill tank

Time $t = \frac{V}{\text{rate}} = \frac{7.693}{1.7} \approx 4.525$
Round to nearest minute: 5 (Note: Correction—original calculation shows ~4.525 rounds to 5, so final answer is 5)

Wait, corrected final answer after rounding: 5.

Step1: Get cylinder radius

$r = 1.4/2 = 0.7$ ft

Step2: Calculate tank volume

$V = 3.14×0.7²×5 = 7.693$ ft³

Step3: Compute filling time

$t = 7.693/1.7 ≈ 4.525 ≈ 5$ minutes

Answer:

10