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Need help with finding density

  1. 1. The problem statement, all variables and given/known data
    Assuming the Earth to be comprised of only a uniform density mantle and a uniform density
    core and the mean density of the mantle to be 4700 kg=m3, determine the mean density of
    the Earth's core. Take Earth's radius to be 6400 km and the radius of the core to be 3500 km.
    Assume the Earth's mean density is 5520 kg=m3

    2. Relevant equations
    density = mass/volume

    3. The attempt at a solution
    V_c = 1.80 * 10^20 meter cubed
    V_e = 1.10 * 10^21 meter cubed
    V_m = V_e - V_c
    = 9.20 * 10^20

    M_e = M_c + M_m
    M_e = D_c*V_c + D_m*V_m
    D_c = (M_e - D_m*V_m)/V_c
    D_c = 9222.22

    I think I got the wrong answer so can someone help me with it.
  2. jcsd
  3. From the givens, I got
    D_c = (M_e - M_m) / V_c
    = [ D_e*V_e - ((D_m (V_e - V_c)) ] / V_c

    which is equivalent to yours and an answer, though slightly different, of the same order of magnitude.
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