Calculating radius of the core with just densities

[bertwan]

Homework Statement

Calculate the radius of the Earth's core using the following data:

Pe = 5,515 kg/m^3 (earth's average density)
Pc = 11,000 kg/m^3 (core's density)
Pm = 4,450 kg/m^3 (mantle-crust density)

Re = 6377km (radius of the earth)

Homework Equations

im guessing we should be using the gravitational equation

g = (GM)/r^2 for different shells (might be wrong)

g= gravitational acceleration
G= Gravitational constant
M = mass of sphere with radius of "r"
r= radius

The Attempt at a Solution

i tried the above equation but got no where with this. i need help!

 

[gneill]

You're dealing with densities, not forces. If the Earth consists of an inner sphere of one density and an outer shell of another density, how would you calculate the average density? Suppose that the inner sphere has radius r_c and that the outer shell extends to radius R_e (radius of the Earth).