Define the unknown volume of the cylinder as
V and the submerged volume as a constant multiplied by
V e.g.
kV.
You can use Archimedes' principle which states that the mass of the object is equal to the mass of the displaced fluid (submerged volume of the object multiplied by the density of the fluid).
Form an equation and solve for
k to obtain the fraction of the cylinder's volume which is submerged.
Your expression should end up as a ratio of the two densities:
k=ρwaterρwood.