Ooh I didn't know there was a new 10" Silent Spinner. Just googled it. However there does seem to be an issue with them breaking (stand not strong enough for wheel) - this video and the comments from others too.
https://www.youtube.com/watch?v=G5kFUx2ZTH8
Melamine lid 1.5cm deep from 35cm tall cage = 33.5 cm. Trixie wheel should just fit.