An ice berg of density $900 kg/m^3$ is floating in water of density $1000 kg/m^3$. The percentage of volume of ice –cube outside the water is ______(%)

Let the total volume of ice –berg is V and its density is $\rho$. If this ice – berg floats in water with volume $V_{in}$ inside it then 

${\mathrm{V}}_{\mathrm{in}}\mathrm{\sigma g}=\mathrm{V\rho g}\Rightarrow {\mathrm{V}}_{\mathrm{in}}=\left(\frac{\mathrm{\rho }}{\mathrm{\sigma }}\right)\mathrm{V} \left({}^{\therefore } \mathrm{\sigma }=\mathrm{density} \mathrm{of} \mathrm{water}\right)$

$\Rightarrow {\mathrm{V}}_{\mathrm{out}}=\mathrm{V}-{\mathrm{V}}_{\mathrm{in}}=\left(\frac{\mathrm{\sigma }-\mathrm{\rho }}{\mathrm{\sigma }}\right)\mathrm{V}\Rightarrow \frac{{\mathrm{V}}_{\mathrm{out}}}{\mathrm{V}}=\left(\frac{\mathrm{\sigma }-\mathrm{\rho }}{\mathrm{\sigma }}\right)=\frac{1000-900}{1000}=\frac{1}{10}$

$\therefore {\mathrm{V}}_{\mathrm{out}}=10\% \text{of Volume}$