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We need to determine how long it will take to drain the cylindrical tank based on the provided dimensions and rate of oil flow.

### Given:
- The tank is a **cylinder**.
- **Length** of the tank, \( h = 4.5 \, \text{ft} \).
- **Diameter** of the tank, \( d = 1.6 \, \text{ft} \), so the **radius**, \( r = \frac{d}{2} = \frac{1.6}{2} = 0.8 \, \text{ft} \).
- **Drainage rate**, \( \text{Rate} = 2.5 \, \text{ft}^3/\text{minute} \).
- **\(\pi \approx 3.14\)** (as instructed in the problem).

### Step 1: Calculate the volume of the cylindrical tank
The formula for the volume \( V \) of a cylinder is:

\[
V = \pi r^2 h
\]

Substitute the values:

\[
V = 3.14 \times (0.8)^2 \times 4.5
\]
\[
V = 3.14 \times 0.64 \times 4.5
\]
\[
V = 3.14 \times 2.88 = 9.0432 \, \text{ft}^3
\]

### Step 2: Calculate the time to drain the tank
The time \( t \) required to empty the tank is given by:

\[
t = \frac{\text{Volume of the tank}}{\text{Rate of drainage}}
\]

\[
t = \frac{9.0432}{2.5} = 3.61728 \, \text{minutes}
\]

Since the answer needs to be rounded to the nearest minute:

\[
t \approx 4 \, \text{minutes}
\]

Thus, it will take approximately **4 minutes** to empty the tank.

---

Do you want further clarification or details on any step? Here are some related questions to deepen your understanding:

1. How is the formula for the volume of a cylinder derived?
2. What would happen if the rate of drainage were slower, say 1 ft³ per minute?
3. How would the time change if the diameter of the tank were doubled?
4. What if the tank were shaped like a cone instead—how would the volume calculation change?
5. How does the value of \(\pi\) affect the result in such problems?

**Tip**: Always double-check units when working with volume and rates in real-life problems to ensure accuracy.

An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4.5 ft long with a diameter of 1.6 ft. Suppose oil is drained at a rate of 2.5 ft³ per minute. If the tank starts completely full, how many minutes will it take to empty the tank?

Learn how to calculate the time to drain a cylindrical oil tank that is 4.5 ft long with a 1.6 ft diameter, using a drainage rate of 2.5 ft³ per minute. This problem involves calculating the volume of a cylinder and applying rate of change to determine the time required. Suitable for high school students in Grades 9-12.

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