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Chapter 1: Problem 59

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

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

Step by step solution

01

Converting area and depth to the same units

Firstly, it's essential to remember that the measurements must all be in the same units when calculating volume. Units of the given surface area are in \(\mathrm{km}^{2}\) while the unit for depth is in meters (\(m\)). The metric system is based on powers of ten, so 1 \(\mathrm{km}\) equals \(10^{3}\) \(\mathrm{m}\). Therefore, the surface area in \(\mathrm{m}^{2}\) will be \(1.8 \times 10^{8}\) \(\mathrm{km}^{2}\) \(\times\) \((10^{3})^{2}\) \(\mathrm{m}^{2}\)/\(\mathrm{km}^{2}\) = \(1.8 \times 10^{14}\) \(\mathrm{m}^{2}\).
02

Calculating Volume

The volume of the Pacific Ocean can be calculated by multiplying the surface area by the depth. So, Volume of Pacific Ocean = Surface Area \(\times\) Depth = \(1.8 \times 10^{14}\) \(\mathrm{m}^{2}\) \(\times\) \(3.9 \times 10^{3}\) \(\mathrm{m}\) = \(7.02 \times 10^{17}\) \(\mathrm{m}^{3}\).
03

Converting Volume to Liters

The volume should be provided in liters, so we need to convert \(\mathrm{m}^{3}\) to \(\mathrm{liters}\). 1 \(\mathrm{m}^{3}\) is equivalent to \(10^{3}\) \(\mathrm{liters}\) (or 1000 \(\mathrm{liters}\)). Therefore, the volume of the Pacific Ocean = \(7.02 \times 10^{17}\) \(\mathrm{m}^{3}\) \(\times\) \(10^{3}\) \(\mathrm{liters}\)/\(\mathrm{m}^{3}\) = \(7.02 \times 10^{20}\) \(\mathrm{liters}\).

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