Infinity 1050w Reference Series 10" 4-ohm subwoofer at Crutchfield.com
Infinity Reference 311a Mono subwoofer amplifier 116 watts RMS x 1 at Crutchfield.com
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If this is the case with the given volume of the box, it will require more watts to achieve the same db output vs a larger enclosure i.e compressing air inside the box as the speaker moves and said resistance is applied to the back of the cone. Not saying the enclosure is too small as it meets the manufacturers guidelines. That being said..
The linked components would be under powered imo due to the 4 ohm sub, and the amp delivering 116w rms in 4 ohm operation. It will work, but the amp would be much happier in 2 ohm operation as it won't be at the upper limit of rms output most of the time when you have the radio cranked. I hope this is not the case. Do you have a link for the sub? I had to guess based on pics and specs you stated. I did see a bunch of links through google that show the amp as 312w without noting that it's 312w @ 2 ohms.
If this is the case and the output is not as expected, change the sub to a 2 ohm one or get a 300w rms amp @ 4 ohms, whichever is cheaper or easier.