why is my hamster biting and chewing on the cage
If your hamster is chewing on the cage bars, it's oftentimes because he wants your attention. Hamsters should get individualized attention every day, even if it just means taking him out of the cage for a little cuddling or time in the exercise ball -- during his waking hours only; don't wake him regularly.
So double the floor size and the width and you're looking at what you need. Bigger than this is always better. If the play area isn't bigger than this, your hamster will chew on the cage to try to escape, it will no matter what kind of chewie you put in there. My hamster did this ceaselessly to her fish tank. You can very cheaply obtain a bin for under 10 dollars at walmart and they make a good, easy to clean, customizable, and fun environment for your hammy to play in.