Question: 
See what I tried below and verify if I'm wrong. I need help here.
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You just need to get the height of the paraboloid (air) in the cylinder. Knowing that the volume of the paraboloid is half of the cylinder of the same height,
$$H_{paraboloid}=2*H_{cylinder}$$
where $H_{cylinder}$ is the height of air when it is not rotating, $0.2\ m$, therefore $$H_{paraboloid}=0.4m=y$$
substituting the value in the equation,
$$y=\frac{\omega^2x^2}{2g}$$
where $x=0.1\ m$, (radius of paraboloid) and $g=9.81\ m/s^2$, you will get
$$\omega=28.014\ rad/s = 267.51 rev/min$$
