Name for air intake hose that goes before the filter

I’m helping a friend with her Prius. While changing the air filter, I accidentally put my finger through(!) an air hose. It appears to be the hose that feeds air into the filter. When I look for “air intake hose” they seem to be talking about the hose going from the filter to the engine.

I’m new to this car, and could use help. Any insight appreciated!

1) what is the name for that hose?
2) where could I find a parts list / blown up diagram for this area?
3) clearly there are some parts where the plastic needs to be replaced. The top of the plastic on the wiper water tank ( or similar ) was also so brittle just touching it made it disintegrate. Are there other known pieces I should look to replace for her?
4) are there aftermarket solutions that might be cheaper?

thanks in advance.

 

Thank you this is what I was looking for.

thank you, that is good to know. We are in the desert, and I’d read it’s better to get the cooler air in there.

Yes, I should have done that. Car is at her house though.

 

I used metal duct tape ( kind made with metal ). I think that will do a decent job. Since the plastic is so degraded, I’ll probably diy something with pvc at some point.