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Chapter 1: Problem 85

The total amount of fresh water on earth is estimated to be \(3.73 \times 10^{8} \mathrm{~km}^{3}\). What is this volume in cubic meters? in liters?

Short Answer

Expert verified
Volume: \(3.73 \times 10^{17}\) m\(^3\), \(3.73 \times 10^{20}\) liters.

Step by step solution

01

Convert Cubic Kilometers to Cubic Meters

To convert the volume from cubic kilometers to cubic meters, recall that:1 ext{ km} = 1,000 ext{ m}.Since the conversion is cubed, we have:1 ext{ km}^3 = (1,000 ext{ m})^3 = 1,000,000,000 ext{ m}^3 = 10^9 ext{ m}^3.Therefore, the volume in cubic meters is given by:\[3.73 \times 10^8 \text{ km}^3 \times 10^9 = 3.73 \times 10^{17} \text{ m}^3.\]
02

Convert Cubic Meters to Liters

To convert the volume from cubic meters to liters, note that:1 cubic meter ( ext{m}^3) = 1,000 liters.Therefore, the volume in liters is:\[3.73 \times 10^{17} \text{ m}^3 \times 1,000 = 3.73 \times 10^{20} \text{ liters}.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cubic Kilometers to Cubic Meters
Volume conversion from cubic kilometers to cubic meters is a vital process in understanding large-scale measurements such as those dealing with planetary resources. When converting cubic kilometers to cubic meters, it's essential to remember the basic conversion factor:
  • 1 kilometer (km) is equal to 1,000 meters (m).
  • Since we are working with volume, which is a three-dimensional measure, we cube the conversion factor: (1 km)鲁 = (1,000 m)鲁.
  • This results in: 1 km鲁 = 1,000,000,000 m鲁 or more simply, 10鈦� m鲁.
For the Earth鈥檚 fresh water calculation: if we have 3.73 脳 10鈦� km鲁 of fresh water, we need to multiply by 10鈦� to convert to cubic meters. This gives us a staggering 3.73 脳 10鹿鈦� m鲁 of fresh water when expressed in cubic meters. With these steps, you can easily convert any volume from cubic kilometers to cubic meters.
Cubic Meters to Liters
Once the volume is expressed in cubic meters, converting it to liters becomes straightforward. This conversion is particularly useful for scientific, industrial, and sometimes even everyday applications. The conversion factor here is:
  • 1 cubic meter (m鲁) equals 1,000 liters.
In our given problem, we have already calculated that the total fresh water is 3.73 脳 10鹿鈦� m鲁.
To find out how many liters this corresponds to, multiply the cubic meters by 1,000. This conversion gives us:
  • 3.73 脳 10鹿鈦� m鲁 脳 1,000 = 3.73 脳 10虏鈦� liters.
Hence, the enormity of the Earth鈥檚 fresh water can also be visualized as 3.73 脳 10虏鈦� liters.
Volume Conversion Steps
Understanding and following the correct steps in volume conversion helps ensure accuracy in calculations. Here's a simple guide for converting between different units:
  • Determine the units you are converting from and to. In this case, cubic kilometers to cubic meters and cubic meters to liters.
  • Identify and apply the relevant conversion factor. Example: 1 km鲁 = 10鈦� m鲁 and 1 m鲁 = 1,000 liters.
  • Multiply your initial volume by these factors step by step, ensuring dimensional consistency.
It鈥檚 also helpful to double-check each step as calculation errors in conversions can lead to significant misunderstandings, especially when dealing with large and small scales. Practicing these conversions with different numbers aids in solidifying these concepts, making them intuitive over time.

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Most popular questions from this chapter

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