Hi there. Sorry to disagree with Scargirl but the cages mentioned are too small and so is a 10 gallon tank. Are you in the US or the Uk as that would help with cage recommendations.
The Imac Fantasy is about the smallest you would want to go and many people consider them too small. They're not ideal as you can't get much depth of substrate in them or have much space for a Syrian sized 27cm wheel. As Pygmypuff says, they do best with bigger continuous floor area and less height.
If you have space for a detolf it would be great! No bars to chew and plenty of space and cheap to buy - £40 in the Uk and $60 in the US - but you do need to make a lid for them out of wood and mesh so there's a bit of diy involved. And they are pretty big - 163 cm long!
To go back to the chewing - if it's bar chewing it's probably because of environment. The key word is 'enrichment' with hammies. Give them as enriched an environment as you can. This includes - space (one continuous space, not lots of smaller sections), depth of substrate - hamsters that have deeper substrate to dig in are less stressed, cage set up and things to relive boredom within the cage set up, a suitable sized wheel so they can run without back pain.
It's like an anxiety stress thing chewing bars usually. Let us know where you are and we can suggest solutions! There are cheaper cage options in the Uk than the US but tanks are cheaper in the US and you can get lids for them as well!
A Zoozone could be a solution if it is bar chewing and she's not the kind of hamster who chews everything in site (eg plastic toys, wheels, houses etc). But the bigger Zoozone 2 is best. The top would need meshing as the bar spacing is 2cm.
I'm guessing you're in the Uk if you're thinking of the Zoozone. A cheaper option would be an Alaska or Barney cage.
http://www.zooplus.co.uk/shop/small_...r_cages/284288
http://www.zooplus.co.uk/shop/small_...r_cages/189303
Both will easily fit an 11" or 12" wheel.
She is unlikely to bar chew in a bigger cage like those, but if you don't want to take the risk then a Zoozone 2 could be a good option or a glass tank, or a detolf.
The Alaska is just over 80cm wide and the Barney is 100cm - both meeting the Uk RSPCA minimum recommended size of 80cm by 50cm. The smallest you would want to go for a Syrian is 70cm by 50cm and that wouldn't be big enough really in my opinion. The Zoozone 1 is about 70cm but wouldn't have the height to fit an 11" wheel, whereas the Zoozone 2 will fit any Syrian sized wheel.
This is our Syrian's cage. It's 80cm x 50cm but I reckon 100cm would be better, as it soon gets cluttered when you put Syrian sized toys in! The base holds 15cm of substrate. If you went for a tank you could put even deeper substrate in and your hammy could dig tunnels! That keeps them happy. Ours can just dig tunnels in 15cm of substrate but not very deep or far. The zoozone is also good for deeper substrate. It actually can work out cheaper or no more expensive, using more substrate because the underneath part stays dry and you just spot clean the top part and need to do big cage cleans less often. If your hamster uses a potty tray you can get away with only doing a big cage clean every 2 months and just spot clean (ie remove and replace the odd wet handful) in between.
http://s1373.photobucket.com/user/ch...l?sort=3&o=134