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You are confusing density with weight. Two pieces of wood of the same density but different sizes have different weights.

Density, you could say, is like hardness. If you take a 6 foot piece of wood, and cut 2 feet from it, the two pieces of wood are definitely different weights but the same hardness. Since they came from the same original piece of wood, they almost have to be the same density.

There are some types of wood that have such high density that they will not float on water.

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