Volume of the material used for making the hollow sphere is,

$V=\frac{4}{3}\pi \left(R^3-r^3\right)$.

For a floating body, buoyance force is equal to the weight of the body. Therefore,

$$\begin{gathered} B=mg \\ \Rightarrow {\rho }_L{V}^{\text{'}}g={\rho }_{S}Vg \\ \Rightarrow {\rho }_L\times \frac{2}{3}\pi R^3={\rho }_S\times \frac{4}{3}\pi \left(R^3-r^3\right) \\ \Rightarrow {\rho }_S=1.14 \mathrm{g} {\mathrm{cm}}^{-3} \end{gathered}$$