Questions: 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 2.4 ft. Suppose gas is poured into the tank at a rate of 2 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.

Solution Steps

The diameter of the cylinder is given as $2.4$ ft. The radius $r$ is half of the diameter: $$r = \frac{2.4}{2} = 1.2 \, \text{ft}.$$

The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h,$$ where $h$ is the height (or length) of the cylinder. Substituting the given values: $$V = 3.14 \times (1.2)^2 \times 3.5.$$ First, calculate $(1.2)^2$: $$(1.2)^2 = 1.44.$$ Now, multiply by $3.14$ and $3.5$: $$V = 3.14 \times 1.44 \times 3.5 = 15.8256 \, \text{ft}^3.$$

Gas is poured into the tank at a rate of $2 \, \text{ft}^3$ per minute. The time $t$ required to fill the tank is: $$t = \frac{V}{\text{rate}} = \frac{15.8256}{2} = 7.9128 \, \text{minutes}.$$ Rounding to the nearest minute: $$t \approx 8 \, \text{minutes}.$$

Final Answer