An open cylindrical vessel filled with water is rotated together with water at angular speed $1 \mathrm{rad} {\mathrm{s}}^{-1}$. At this angular speed, the centre of the bottom is just exposed. If the angular speed is increased to $\sqrt{\frac{3}{2}} \mathrm{rad} {\mathrm{s}}^{-1}$, how much area (in ${\mathrm{cm}}^2$) of the bottom of the vessel is now exposed to surrounding? [Area of the cross-section of cylinder is $27 {\mathrm{cm}}^2$]