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The radius of the Earth is approximately 6370 km. If one could dig down straight towards the center of the Earth, one would find that the outermost 2890 km (the crust and the mantle) has an average density of about 4.5 g/cm3. Farther down is the core. If the average density of the Earth is 5.5 g/cm3, what is the average density of the Earth's core? (Recall that the volume of a sphere is given by V = (4/3)πr3.)

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    volume of earth is 4/3 pi * 6370^3 = 10.8270*10^11 km^3
    volume of core is 4/3 pi * (6370-2890)^3 = 1.7653*10^11 km^3
    volume of crust+mantle is thus 9.0617*10^11 km^3

    5.5*10.8270*10^11 = 4.5*9.0617*10^11 + d*1.7653*10^11
    d = 10.6 g/cm^3

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