Wouldn't a square one mix far better?
Not necessarily, why do you think a washing machine's washing basket/tub is round? When you get a load that is not centered properly, the washing machine will start to bang against itself, eventually doing damage to itself. It is the same idea with the cement mixer, except you have tons of material to be working with. How you like to be the one to answer to your boss saying that the spinning action of the mixer is broken and we can't get all the cement out before it hardens? That's why circular shapes gives us nice smooth tangents, yet it still mixes our cement.
Actually, the inside of the mixer is not round, it has a series of spiral blades which when the the drum is turning the way you normally see it are evenly mixing contents which are usually loaded separately - sand, water, cement, aggregate and any chemicals - and mixed while moving. The shape of the blades is matched to the amount of air normally added to the mix.
Actually a square mixer would have many cons: cement would get stuck in corners and dry, Only a fifth of the cement originally put in would be able to be poured out because it would dry... depending on the type. If you think about it, as more and more cement dried in the corners it would naturally turn into a round inside. So a round mixer is just the more natural way to go and is much easier to clean and keep working well.
It would vibrate too much and unmixed cement would become trapped in the corners.
