We can solve this problem using the fact that the volume of liquid in a cylindrical tank is proportional to the height of the liquid. Given that the tank holds 420 gallons when filled to a depth of 8 feet, we can calculate how many gallons are in the tank when the oil is at a depth of 5.5 feet.

Step 1: Find the volume per foot of depth.

The total volume of the tank is 420 gallons when the depth is 8 feet. The volume per foot of depth is:

$\text{Volume per foot} = \frac{420 \, \text{gallons}}{8 \, \text{feet}} = 52.5 \, \text{gallons per foot}$

Step 2: Calculate the volume for 5.5 feet.

To find how many gallons are in the tank when the depth is 5.5 feet, multiply the volume per foot by the new depth:

$\text{Volume for 5.5 feet} = 52.5 \, \text{gallons per foot} \times 5.5 \, \text{feet} = 288.75 \, \text{gallons}$

Step 3: Answer

So, when the depth of oil is 5.5 feet, there are 288.75 gallons in the tank.

Would you like more details on the steps or have any questions?

Here are 5 related questions to expand on this problem:

1. How would the volume change if the tank had a different diameter?
2. How can we calculate the volume of a cylindrical tank if only its radius and height are known?
3. What would happen if the tank were partially filled with water, and we wanted to know the oil volume?
4. How can this method be applied to tanks of different shapes?
5. How would you adjust the calculation if the depth were measured in meters instead of feet?

Tip: When working with cylindrical volumes, always remember the formula $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height of the liquid.