A 3.0 cm thick layer of oil (density $$\rho_{oil} = 800\ \text{kg/m}^3$$) floats on water (density $$\rho_w = 1000\ \text{kg/m}^3$$) in a transparent glass beaker. A solid cylinder is observed floating vertically with $$\frac{1}{3}$$ of it in water and $$\frac{1}{3}$$ in the oil. Oil is gently poured into the beaker until the cylinder floats in oil only. The fraction of the solid cylinder in oil now is