Final answer:
The volume of Earth is 10^21 m^3, which converts to 10^12 km^3, approximately 10^9 mi^3, and 10^27 cm^3 when using appropriate conversion factors. The correct options are a, b, and c.
Step-by-step explanation:
Turning our attention to unit conversion, particularly volume conversion, it is important to consider the vast differences in scale when converting from cubic meters to other units of volume. In this instance, we are starting with Earth's volume, which is approximately 1021 m3.
Understanding Conversion Factors
The conversion factor from meters to kilometers is as follows: there are 1,000 meters in a kilometer. Therefore, to convert from cubic meters (m3) to cubic kilometers (km3), the conversion factor of 1,000 is cubed, resulting in 1 billion (109) cubic meters in one cubic kilometer. Using this conversion factor, we can calculate the volume of Earth as follows:
1. 1021 m3 divided by 109 equals 1012 km3
To convert cubic meters to cubic miles, we utilize the factor that 1 mile is approximately 1.609 kilometers, thus there are (1.609)^3 cubic kilometers in one cubic mile. Employing this conversion:
1. 1012 km3 divided by (1.609)^3 equals approximately 109 mi3
For conversion to cubic centimeters, it is vital to note that one cubic meter equals 1,000,000 cubic centimeters (cm3). Therefore:
1. 1021 m3 times 106 equals 1027 cm3
Summarized, the correct options for volume conversions are:
• a) 1012 km3
• b) 109 mi3
• c) 1027 cm3