Question

the empty gas tank of a truck needs to be completely filled. the tank is shaped like a cylinder that is 3 ft long with a diameter of 1.8 ft. suppose gas is po 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 of cylinder

The diameter is 1.8 ft, so radius $r = \frac{1.8}{2} = 0.9$ ft.

Step2: Compute tank volume (cylinder)

Use volume formula $V = \pi r^2 h$. Substitute $\pi=3.14$, $r=0.9$, $h=3$:
$$V = 3.14 \times (0.9)^2 \times 3$$
$$V = 3.14 \times 0.81 \times 3 = 7.6302 \text{ ft}^3$$

Step3: Find fill time

Time = $\frac{\text{Volume}}{\text{Fill rate}} = \frac{7.6302}{2.3}$
$$\text{Time} \approx 3.3175$$

Step4: Round to nearest minute

Round 3.3175 to the nearest whole number.

Answer:

3 minute(s)