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## Homework Statement

A planet with R=4000km and [tex]\rho[/tex]

_{avg}=5g/cm

^{3}. The planet is made of quartz all the way to the core, which is made of iron. The densities of quart and iron are [tex]\rho[/tex]

_{quartz}=2.65g/cm

^{3}and [tex]\rho[/tex]

_{iron}=7.874g/cm

^{3}. Calculate the radius of the core.

## Homework Equations

[tex]\rho[/tex]=M/V

V

_{sphere}=4/3[tex]\pi[/tex]r

^{3}

## The Attempt at a Solution

I solved for M

_{planet}=[tex]\rho[/tex]

_{avg}=5g/cm

^{3}*4/3[tex]\pi[/tex]4000km and got 1.34*10

^{27}g. Then with assuming the M

_{planet}=M

_{Tot. Qrtz}+M

_{Tot. Iron}, I tried using various substitutions of my unknowns and I can't get anywhere close to being able to solve for any of them. I know it's some simple calculus, but I am lost and don't remember how to do this. The biggest problem for me is that the radius is cubed and I forgot what to do to solve for that.

Any fresh ideas would help a lot.

Thanks