A 3.0 cm thick layer of oil (. density . _ oil =800 ~kg / m^3)...

A 3.0 cm thick layer of oil $\left(\right.$ density \left.\rho_{\text {oil }}=800 \mathrm{~kg} / \mathrm{m}^3\right)$floats on water \left(\right.$ density \left.\rho_{\mathrm{w}}=1000 \mathrm{~kg} / \mathrm{m}^3\right)$in a transparent glass beaker. A solid cylinder is observed floating vertically with$\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