Good test TM. It's always bugged me to run a motor without a filter like sleds do stock. Enough so that it is one of the first things I take care of to prepare a sled for my to use.
The foam material you pictured looks like what I have used over the years to seal the joints and install behind the intake screens to finish filtering what the screen material lets through and to seal the hard plastic frame of these intakes to hood also.
I get this stuff at my local hardware store, cheap lol. It's humidifier foam and comes in a few colors lol, thicknesses and densities. I use about the same density as you pictured and pick the purdy yellow color.
Intake sealing for my Pro from the bottom up.
Drain holes. Need 'em (less so if sealed completely), can't seal them, so I make them bigger and use a drain hose from a dirt bike. Usually find one for a buck at a bike bone yard.
Top and bottom halves. Install shelf, then I used contact cement on the shelf to install a 3/16"x3/4" closed cell evo based foam around the perimeter with a bit of overhang to the outside. Very resilient and tough. I have a 50' roll from some time ago and don't remember where I got it lol. One of the local mines I think.
First time you snap it shut is a bit tough but then it takes a "mold" to the little ridges and works so well you wonder why it isn't stock lol.
Tube. My sled came with a double wrap of sealed cell foam on the bottom but only one on the top. I thought the bottom was good enough but needed a bit more downward pressure with the hood installed.
So I cut out 2 square outer rings of the foam you pictured, contact cemented (3M foam spray) one to the hood and one to the top of the tube. Now when the hood is installed the extra foam provides more pressure to seal the bottom and the extra thickness seals the top.
Hood and plenum. Tough part but nothing like trying to seal a flexy, heavy PC hood lol.
Separate the hood and plenum and throw away the noise horns (my personal opinion), then start in he middle at the front to re-attach.
As your working your way to the front in both directions snapping it together but before you get too far along, start sealing it with a 3/4" strip of quality duct tape (good stuff means just once, cheap stuff means maybe again) until you get right around to the "U" where the steering stem needs clearance.
This spot gets some flex stressing so here, I used a bit of a bead of silly stuff and fastened the two halves together with 4 1/8" aluminum rivets with a burr on the inside. It will be obvious where you need to put them. You can even use a magic marker to color match to the hood if you want lol.
Intakes screens. These let stuff through too. Especially at the joints-edges. Here I take that foam and cut out a piece to fit on the backside of the screen but a little oversize on the outside edges (now it filters like yours shows in pic).
Try to install and the foam will show to be too thick. a little trimming with sissors on a 45 degree angle and eventually they snap in good with a seal to the hood. Then trim the outside with a utility knife.
Now your ready for a dusty day lol. In honesty my favourite sleddin days are the "dusty" ones with the sun sparkling through that dust lol. Last thing I want to worry about is my motor eating that dust.
I've done this for a while and when I preped my Pro the first time it was part of must do stuff for me. Now that it has proven itself it has become a keeper,,, I'm very happy snowdust is not washing away my oil on the walls and the other dusts not scoring them.
Hope it helps.