8” woofer for 45L sealed box. 3way designed crossed at app. 800hz.

11.5" are 29cm. You will find a lot of 10" woofer that fit that baffle and work with the large volume you got. If you got the volume, use it.
You may tell a little more about your plans, because the woofer should not have more SPL than the other 2 speakers. Do you know how to do a crossover? Maybe do a search for "3-way speaker" or the like.
 
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The SB Acoustic SB23MFCL45-4 is a great driver with large Xmax and low distortion. NOTE this is the 4 Ohms version - do not get the 8 Ohms version. It's about $150 though.

45L is a bit too much volume for most 8 Ohm drivers so overall the Q will be on the low side (drooping response). For example, in 45L the SB driver has Q=0.45 with F3=61Hz, F10=27Hz. You could add 2 Ohms series resistance to get Q up to 0.575 and then F3=37, F10=22Hz but sensitivity will go down from 88Db to 85dB at 2.83V.

As others have posted, a 10" driver will likely work better in 45L...
 
You really need a woofer with a Qts of near 1.0 for that size sealed box. GRS 8PR-8 ($14) would work in 25L, you could fill with some wood blocks to reduce volume. Goldwood GW-8028 ($32) may work too but works better in a 35L box.
Back to 10" and you have the Peerless SLS 10" 830668 ($60) would enjoy a 45L sealed enclosure with F3 around 47Hz, the 8" version works best around 28-30L.
 
Dayton RS225-4 and RS225-8... both will play nicely with an 800 Hz crossover. They have low distortion, and reasonable Xmax. They are in your price range.

RS225-4 in 45 liter sealed box: 4 Ohm, F3=59 Hz, F10=29 Hz, Qtc=0.59, sensitivity (2-pi) = 91 dB

RS225-8 in 45 liter sealed box: 8 Ohm, F3=57 Hz, F10=27 Hz, Qtc=0.57, sensitivity (2-pi) = 87 dB

You could use any box size from 20 to 50 liters with only a small change in bass performance.

I recently used the RS225-8 with a passive radiator, and I thought it was a very good value... A high quality speaker for the money.
 
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I would really like to keep the cabinet as small as possible. Using a passive radiator is not a bad idea. Right now I just putting a concept together. Cost is one aspect, getting so decent sound is the main thing, of course, but I don’t see why using decent low cost drivers would not work. I have some Cambridge soundworks model 6s , not great , but very comfortable to listen to. I don’t think the drivers in them cost much, but they are well thought out, for what they are.
 
I am gathering information right now, and looking at what others have done. I have no intention of rediscovering the wheel. They will just be another rendition of the old three way “ book shelf” , but will live on stands. Looking for f3 around 40hz
 
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