To determine the thickness of the resulting oil slick, we need to follow a methodical approach. Let's break down the solution into clear steps.
### Step 1: Convert the volume of oil to cubic centimeters
We are given that the volume of oil is 1.06 quarts. We also know that 1 quart equals 1000 cm³. Therefore, the volume of oil in cubic centimeters is:
[tex]\[ 1.06 \text{ quarts} \times 1000 \text{ cm}^3/\text{quart} = 1060 \text{ cm}^3 \][/tex]
### Step 2: Calculate the area of the swimming pool in square centimeters
The swimming pool's dimensions are given in meters: 25.0 m in length and 30.0 m in width. We need to convert these measurements to centimeters since the volume of oil is already in cubic centimeters. There are 100 centimeters in a meter, so:
[tex]\[ \text{Length in centimeters} = 25.0 \text{ m} \times 100 \text{ cm/m} = 2500 \text{ cm} \][/tex]
[tex]\[ \text{Width in centimeters} = 30.0 \text{ m} \times 100 \text{ cm/m} = 3000 \text{ cm} \][/tex]
Now, we can find the total area of the swimming pool in square centimeters:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} = 2500 \text{ cm} \times 3000 \text{ cm} = 7,500,000 \text{ cm}^2 \][/tex]
### Step 3: Calculate the thickness of the oil slick
The thickness of the oil slick can be found by dividing the volume of oil by the area of the pool. We can use the formula for the thickness ([tex]\( t \)[/tex]) as follows:
[tex]\[ t = \frac{\text{Volume of oil}}{\text{Area of the pool}} \][/tex]
Substituting in the known values:
[tex]\[ t = \frac{1060 \text{ cm}^3}{7,500,000 \text{ cm}^2} \][/tex]
### Step 4: Simplify to find the thickness
[tex]\[ t = \frac{1060}{7,500,000} \approx 0.00014133333333333334 \text{ cm} \][/tex]
### Final Answer
The thickness of the resulting oil slick is approximately [tex]\( 0.000141333 \)[/tex] cm.
This detailed step-by-step process allows us to break down the problem into manageable parts and find the solution effectively. The outcome is an extremely thin layer of oil on the surface of the swimming pool.
