Converting Earth's Radius to Surface Area and Volume | Conversion Help

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SUMMARY

The Earth's radius is 6.37x106 meters. To calculate the surface area and volume of the Earth, use the formulas for a sphere: surface area is 4πR2 and volume is (4/3)πR3. After calculating the surface area in square meters, convert it to square kilometers using the conversion factor 1 km2 = 106 m2. Similarly, apply the conversion for volume to obtain the result in cubic kilometers.

PREREQUISITES
  • Understanding of basic geometry, specifically the properties of spheres.
  • Familiarity with the mathematical constants π (pi).
  • Knowledge of unit conversion, particularly between square meters and square kilometers.
  • Ability to perform arithmetic operations involving exponents.
NEXT STEPS
  • Study the derivation of the formulas for surface area and volume of a sphere.
  • Practice unit conversion techniques for both area and volume.
  • Explore applications of these formulas in geophysics and environmental science.
  • Learn about the significance of Earth's measurements in climate modeling and geography.
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Students in mathematics or physics, educators teaching geometry, and anyone interested in Earth sciences or environmental studies.

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Homework Statement


The Earth's radius is 6.37x10^6 meters. I need to convert this to surface area in km^2 and it's volume in cubic kilometers.


I'm not sure where to start on either one.



Thanks
Jason
 
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Do you know the formula for the surface area/volume of a sphere?
 
Surface area is 4pi R^2 and surface volume is 4pi R^3
 
Darkhrse99 said:
Surface area is 4pi R^2 and surface volume is 4pi R^3

Note that the volume is \frac{4}{3} \pi r^3

So just put the radius into the formulas and for the surface area, the answer will be in m2. To convert, think of it like this:


1km2=1km*1km=1000m*1000m=106m2

Hence 1km2=106m2

Similary do the same for 1km3 and you'll get it out.
 
Thanks.
 

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