Answer:
r = [3 * (pAl/MAl)]/(4 * pi)]^1/3
r = [3 * (pFe / MFe)]/(4 * pi)]^1/3
Step-by-step explanation:
In the equilibrium state, aluminum and iron have the same mass. From the density equation and solving for the mass we have:
Mass = density/volume
MFe = pFe/V
MAl = pAl/V
In equilibrium, we have that MFe = MAl
Solving for the volume:
MFe = pFe/V
V = pFe/MFe
MAl = pAl/V
V = pAl/MAl
The equation for the volume of a sphere is equal to:
V = (4 * pi * r^3)/3
Replacing the volume of both iron and aluminum, we have:
V = (4 * pi * r^3)/3
r = [(3 * V)/(4 * pi)]^1/3
r = [3 * (pAl/MAl)]/(4 * pi)]^1/3
r = [3 * (pFe/MFe)]/(4 * pi)]^1/3