The density of earth

This post gives information on the radius and the weight of the earth and ask reader to calculate the density of the earth.  

Question:  What is the density of earth given its radius 6371 kilometers and its mass 5.972 x 10¹² kilograms?

Sources:

Wikipedia article provides formulas pertaining to a sphere.

http://en.wikipedia.org/wiki/Sphere

Scientific American story finds that the earth is not a perfect sphere.

http://www.scientificamerican.com/article.cfm?id=earth-is-not-round

A Wikipedia article provides information on the radius and shape of the earth.

http://en.wikipedia.org/wiki/Earth_radius

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)