Answer
$\rho = 1300~kg/m^3$
Work Step by Step
In part (a), we found that the mass of the sphere is $~~1.2~kg$
We can find the volume of the material used to make the sphere:
$V = \frac{4}{3}~\pi~r_2^3-\frac{4}{3}~\pi~r_1^3$
$V = \frac{4}{3}~\pi~(r_2^3-r_1^3)$
$V = \frac{4}{3}~\pi~[((0.090~m)^3-(0.080~m)^3]$
$V = 0.000909~m^3$
We can find the density:
$\rho = \frac{m}{V}$
$\rho = \frac{1.2~kg}{0.000909~m^3}$
$\rho = 1300~kg/m^3$