Altough the wood is dense, the water still applies an upwards force to it. 
A boat can float on water because the surface in contact with the boat in an upward direction provides enough force to stop it from sinking. To achieve this effect, the boat does not have a flat bottom but a sloping one. The deeper the ramp goes into the water, the more force the water exerts to keep the boat afloat. The surface of the ramp allows for more water to contact the boat to create that upwards force.

In short: the slope angle is more important than the material used to build the boat, to keep it afloat.
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