Problem 90 The surface area and average dep... [FREE SOLUTION] (2024)

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To calculate the volume of the Pacific Ocean, we first need to convert the surface area from square kilometers to square meters. The given surface area is \(1.8 \times 10^8\) square kilometers. Here's why and how we convert it:

1. **Conversion Factor**: We know that 1 kilometer (km) equals 1000 meters (m).
2. **Conversion Process**: When converting square kilometers to square meters, we need to account for the squared units:

• \(1 \text{ km}^2 = (10^3 \text{ m})^2\)
• \(1 \text{ km}^2 = 10^6 \text{ m}^2\)

3. **Apply the Conversion**: Multiply the surface area in square kilometers by \(10^6\).
\[1.8 \times 10^8 \text{ km}^2 \times 10^6 = 1.8 \times 10^{14} \text{ m}^2\]
Now, we have the surface area in square meters which we will use in the volume calculation.

With the converted surface area, we next calculate the volume of the Pacific Ocean by considering its average depth. The given average depth is \(3.9 \times 10^3\) meters. For volume calculation, we use the formula:
\[\text{Volume} = \text{Surface Area} \times \text{Depth}\]
Here's how:

1. **Substitute Known Values**: The surface area is \(1.8 \times 10^{14} \text{ m}^2\) and the depth is \(3.9 \times 10^3 \text{ m}\).
2. **Calculate**:
\[1.8 \times 10^{14} \text{ m}^2 \times 3.9 \times 10^3 \text{ m} = 7.02 \times 10^{17} \text{ m}^3\]
Thus, the volume of the Pacific Ocean in cubic meters is \(7.02 \times 10^{17} \text{ m}^3\). This step gives us the volume in cubic meters, which is essential for the final conversion.

Finally, to determine the volume of the Pacific Ocean in liters, we convert the volume from cubic meters to liters. The conversion factor here is straightforward, as 1 cubic meter equals 1000 liters.

1. **Volume in Cubic Meters**: We have \(7.02 \times 10^{17} \text{ m}^3\).
2. **Conversion Factor**: 1 cubic meter equals 1000 liters.
3. **Apply the Conversion**:
\[7.02 \times 10^{17} \text{ m}^3 \times 10^3 = 7.02 \times 10^{20} \text{ liters}\]
Therefore, the volume of the Pacific Ocean is \(7.02 \times 10^{20} \text{ liters}\). By understanding and applying these unit conversions properly, we can find the volume in whatever unit is required for interpretation.