How Do You Calculate the Density of Earth's Core Given Its Mantle Density?

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SUMMARY

The mean density of Earth's core can be calculated using the provided values for the mantle and Earth's overall density. Given the mantle density of 4700 kg/m³, Earth's mean density of 5520 kg/m³, and the respective volumes of the core and Earth, the core density (D_c) is determined to be approximately 9222.22 kg/m³. The calculations involve using the formula for density, mass, and volume, specifically applying the equation D_c = (M_e - D_m * V_m) / V_c. This approach confirms the core's density is significantly higher than that of the mantle.

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Homework Statement


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


Homework Equations


density = mass/volume


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.
 
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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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