Answer
$V=6.43\times10^{-4}~m^3$
$\rho=2.78\times10^3~kg/m^3$
Work Step by Step
Sum all the forces when the rock is submerged in water to find the Buoyant force:
$\sum F=T+B-W=0$
$11.2~N+B-17.5~N=0$
$B=6.3N~$
Find the volume:
$B=\rho_w V g$
$\rho_w=1000~kg/m^3$
$V={B \over \rho_w g}={6.3~N \over (1000~kg/m^3)(9.8~m/s^2)}=6.43\times10^{-4}~m^3$
Find the Desity:
$\rho={m\over V}$
$m={17.5~N \over 9.8~m/s^2}$
$\rho={17.5~N\over(6.43\times10^{-4}~m^3)(9.8~m/s^2)}=2.78\times10^3~kg/m^3$
