Answer
$0.956\;cm$
Work Step by Step
Let $r$ be the radius of the ball. As the ball is made of Fe, the density of the ball has been taken taken as $\rho_b=7.9\;g/cm^3$
According to Archimedes’ principle the buoyant force is equal to the total weight of the cylinder and the ball
$F_b=W$
or, $ρ_wgVsub=mg$
or, $ρ_wgVsub=\rho_cV_cg+\rho_bV_bg$
or, $ρ_wVsub=\rho_cV_c+\rho_bV_b$
or, $1\times(4\times12+V_b)=0.3\times6\times12+7.9\times V_b$
or, $6.9V_b=48-21.6$
or, $V_b=3.83\;cm^3$
or, $\frac{4\pi r^3}{3}=3.83$
or, $\boxed{r=0.956\;cm}$
