Question: What is the density of earth given its radius 6371 kilometers and its mass 5.972 x 1012 kilograms?
Wikipedia article provides formulas pertaining to a sphere.
Scientific American story finds that the earth is not a perfect sphere.
A Wikipedia article provides information on the radius and shape of the earth.
Answer: The answer to this question is based on the assumption that earth is a perfect sphere. It is close to but not perfectly spherical.
The formula for the volume of the sphere is
Volume of earth=(4/3) x pi x r3
Plugging r=6371 into the volume formula we get
Volume=(4/3) x 3.1416 x 63713 or 1.083 x 1012.
The density is mass divided by volume
=5.972 x 1024/1.083 x 1012
=5.513 x 1012 (KG/KM3)
Convert (kg/km3) to (g/cm3)
Multiply the numerator by 1,000. (There are 1,000 grams in a kilogram.)
Multiply the denominator by 100,0003 or 1.0x 1015 (There are 100,000 centimeters in a kilometer.)
We get 5.513 (g/cm3)
This post has a follow up post on the ratio of densities.
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