Hi all, I am having a hard time finding the name and part# of this hose. It is hidden behind the battery and it connects the air filter box to the radiator(I think?). I have attached a photo with the battery removed. Sorry about the poor quality picture. Can anyone identify this? Any help is much appreciated!

https://i.imgur.com/Iq0eZA7.jpg

side note: could this faulty hose be giving me poor gas mileage?

 

[UPDATE]

Found the part in another forum. Part #10 in the diagram and Volvo part# 30620749 in case anyone is interested.

 

That is good to know. It's the cold air inlet to the air cleaner housing. Mine is cracking and looks like it could collapse from low pressure at any moment.