Answer:
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since the volume of oil in the tank is directly proportional to the depth of the oil, we can calculate the amount of oil left in the tank when it is 3 feet deep using a simple ratio.
First, we need to convert the tank's capacity from gallons to cubic feet because our measurements are in feet. According to the U.S. liquid gallon to cubic foot conversion, 1 gallon is approximately 0.133681 cubic feet. So, the tank's total volume in cubic feet is 620 gallons * 0.133681 cubic feet/gallon.
Let's denote the total volume of the tank as V_total and the remaining volume when the tank is 3 feet deep as V_remaining.
V_total = 620 * 0.133681 cubic feet.
Given that the total height (h_total) of the tank is 8 feet and the remaining height (h_remaining) is 3 feet, we can set up the following proportion:
h_remaining / h_total = V_remaining / V_total.
By cross-multiplying and solving for V_remaining, we can find the remaining volume in the tank when it's 3 feet deep. Then, we convert this volume back to gallons by dividing by 0.133681.
Let's calculate that.
Apologies for the confusion; I made a mistake. I can't execute calculations directly in this manner. I'll carry out the calculations below instead:
The total volume of the tank in cubic feet is:
V_total = 620 gallons * 0.133681 cubic feet/gallon = 82.9022 cubic feet.
The remaining volume when the tank is 3 feet deep can be calculated with the proportion:
h_remaining / h_total = V_remaining / V_total.
After cross-multiplying and solving for V_remaining, we have:
V_remaining = (h_remaining / h_total) * V_total = (3 ft / 8 ft) * 82.9022 cubic feet = 31.0941 cubic feet.
Then, we convert this volume back to gallons by dividing by 0.133681:
V_remaining_gal = 31.0941 cubic feet / 0.133681 = 232.63 gallons.
Rounding to the nearest whole number, approximately 233 gallons remain in the tank when the depth of the oil is 3 feet.