*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 10

^{12}kilograms?

**Sources:**

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 r

^{3}
Plugging r=6371 into the volume formula we get

Volume=(4/3) x 3.1416 x 6371

^{3}or 1.083 x 10^{12}.
The density is mass divided by volume

=5.972 x 10

^{24}/1.083 x 10^{12}
=5.513 x 10

^{12 }(KG/KM^{3})
Convert (kg/km

^{3}) to (g/cm^{3})
Multiply the numerator by 1,000. (There are 1,000 grams in a kilogram.)

Multiply the denominator by 100,000

^{3 }or 1.0x 10^{15}(There are 100,000 centimeters in a kilometer.)
We get 5.513 (g/cm

^{3})

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