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The characteristic of wood that density affects in woodworking is its strength and workability. Density is a crucial factor as it influences the structural integrity of the wood; denser woods typically exhibit greater strength, making them suitable for applications that require the material to withstand significant loads or stresses. Additionally, the density affects how the wood is machined and finished.

For example, denser woods may require different tools or techniques during cutting and shaping due to their hardness, while lighter woods may be easier to work with but less durable. Understanding the relationship between density and these properties is essential for woodworkers as it guides their selection of wood for specific projects based on the demands of the work being completed.

The other options are less directly related to the impact of density in woodworking: color is determined by the species and finish of the wood rather than its density; cost is influenced by various factors including wood type, availability, and market demand; and length is not affected directly by density, as it pertains to how the wood is cut rather than its inherent properties.