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.