By white ring I assume you mean the
Big Fat Cross (BFC), the area of tiles a city can work. Cottages that cannot be worked by a city are utterly useless as they're only function is to increase

gained from
working a tile same with farms increasing

. This applies to all tiles if they do not bring a resource (if its a mine on copper then its very useful!).
To an extenet this also includes tiles within the cities workable area!
If your happy cap

) cap)allows 4 population, and you've built 4 cottages 2 farms 3 mines and a fishing boat then you can only work up to 4 of those tiles till your

cap is increased.
Due to this its best to improve only tiles your city will be working either immediately, OR in the very near future OR if your workers really have nothing better to do.