Question

The surface area and average depth of the Pacific Ocean are \(1.8 \times 10^{8} \mathrm{~km}^{2}\) and \(3.9 \times 10^{3} \mathrm{~m}\), respectively. Calculate the volume of water in the ocean in liters.

Short answer

The volume of water in the Pacific Ocean is \( 7.02 \times 10^{20} \) liters.

Step-by-step solution

Convert Depth to Kilometers

First, convert the average depth from meters to kilometers. Since 1 kilometer equals 1000 meters, divide the depth by 1000: \( \frac{3.9 \times 10^3 \text{ meters}}{1000} = 3.9 \text{ kilometers} \).

Calculate Volume in Cubic Kilometers

To find the volume of the Pacific Ocean in cubic kilometers, multiply the surface area by the depth: \( 1.8 \times 10^8 \text{ km}^2 \times 3.9 \text{ km} = 7.02 \times 10^{8} \text{ km}^3 \).

Convert Volume to Liters

To convert cubic kilometers to liters, use the fact that 1 cubic kilometer equals \( 10^{12} \) liters. Multiply the volume in cubic kilometers by \( 10^{12} \): \( 7.02 \times 10^{8} \text{ km}^3 \times 10^{12} = 7.02 \times 10^{20} \text{ liters} \).

Key concepts

Surface Area

The surface area of an object is the total area that the surface of the object occupies. It is measured in square units such as square meters (\(\text{m}^2\)) or square kilometers (\(\text{km}^2\)). Surface area is crucial for volume calculations, especially when dealing with large bodies of water like oceans.

For the Pacific Ocean, its vast surface area is given as \(1.8 \times 10^{8} \text{ km}^2\). Understanding the size of this surface area helps in calculating the total volume of water the ocean holds. To put it into perspective:

• It's like spreading out an enormous sheet that covers many countries combined!
• The surface area is what you see from above, like if you were on a satellite looking down at the ocean.

The importance of knowing the surface area can be linked to various factors such as environmental impact, marine biodiversity, and global climatic patterns.

Depth Conversion

Converting depth from meters to kilometers is simple yet crucial in understanding large measurements. Since 1 kilometer is equal to 1000 meters, converting depth units helps simplify calculations when dealing with extreme depths found in oceans.

In the problem, the depth of the Pacific Ocean is given as \(3.9 \times 10^{3} \text{ meters}\). By dividing by 1000, we convert this to kilometers, resulting in \(3.9 \text{ kilometers}\).

• Why convert? It makes large numbers more manageable in calculations.
• Simplicity in units ensures accuracy and uniformity in further mathematical operations.

Getting familiar with depth conversion aids in calculating larger volumes accurately, essential for many scientific and commercial applications.

Cubic Kilometers to Liters

Once we have calculated the volume of the water in cubic kilometers, the next step involves converting this volume into liters. The sheer size of cubic kilometers can be challenging to visualize, which is why converting to liters, a more relatable unit for fluid measurement, is beneficial.

One cubic kilometer contains \(10^{12}\) liters, so when you have a volume of \(7.02 \times 10^{8} \text{ km}^3\), you multiply by \(10^{12}\) to convert it into liters. The equation will be:

• Volume in liters = Volume in cubic kilometers \(\times 10^{12}\)
• This gives \(7.02 \times 10^{20} \text{ liters}\) – an immense quantity reflecting the vastness of the Pacific Ocean.

Understanding this conversion helps relate oceanic volumes to everyday uses of water and better comprehend the vast capacities involved in nature.