Almost all U.S. LTL carriers use NMFC freight classes, although some are attempting to move to a dimensionally-based system.

No. If you claim that your freight is a lower class than it actually is, your carrier will likely find out. They will charge you a fee for reclassifying the freight and charge you the appropriate amount for the actual class of your freight after it has been shipped.

Density is the relationship between weight and size. A ping pong ball, which is very little material surrounding a good amount of air, is low density. Bricks, which are heavy for their size, are high density. In LTL shipping, it is commonly measured in pounds per cubic foot.