160mm is huge, and 160mm I have never hear of either, that one is 120mm and is the best one around for the price, it is $39.99, that's an insane cooler for the price and I wouldn't go anything cheaper to be honest, putting the extra $4.99 is defiantly worth it.
That is why i suggest getting the cooler master Hyper 212 EVO, It'll fit but is $39.99, best in it's range by a long shot.
The hyper 212 is 159mm tall. It won't fit. The Hyper TX3 will fit and is a decent little cooler for a 3570k. It is far better than stock. I used one for a build because Microcenter had an open box one for like $10 and it fit the person's budget well enough that we were allowed to get a better motherboard for the build.