Final answer:
The volume of Earth, given as 10³° m³, converts to 10²¹ km³ and 10³⁶ cm³ using the conversion factors between cubic meters, cubic kilometers, and cubic centimeters.
Step-by-step explanation:
The given volume of Earth is on the order of 10³° m³. To convert this figure into cubic kilometers (km³) and cubic centimeters (cm³), we need to apply the conversion factor between the units of volume based on the conversion factor of their corresponding length units.
To convert cubic meters to cubic kilometers, note that 1 km³ is equal to (1000 m)³, or 10⁹ m³. Therefore, to convert meters cubed to kilometers cubed, we divide by 10⁹:
10³° m³ / 10⁹ m³/km³ = 10²¹ km³
To convert cubic meters to cubic centimeters, we use the fact that 1 m³ is equal to (100 cm)³ or 1,000,000 cm³. So to convert to cubic centimeters, we multiply by 1,000,000:
10³° m³ × 1,000,000 cm³/m³ = 10³⁶ cm³