Typically a hutch or a cage.
in a cage.
A cage. One with something they can hide in.
A hutch.
If you have a big open space or back yard you should purchase a rabbit hutch or if you wish to keep your rabbit indoors you should purchase a rabbit cage. Whatever you do, make sure you keep the rabbit safe! Rabbits need exercise daily, but there are many dangers to them both inside and outside. It's up to the rabbit owner to control the rabbit's environment. For details, see the related questions below -- they have lots of information and helpful links.
In a hutch, pen, cage, or run in your garden or inside the house.
hutch
hutch
That would be its cage or hutch.
a hutch
Yes, keep your rabbit inside if you live where its very cold or hot.
Not really - most rabbits can be kept either outside or inside. Some people keep small rabbits inside because they are more vulnerable outside. Some people also keep larger rabbits inside because they are more like dogs.
Rabbits have a lot of preditors. Some of them can be dogs, snakes, racoons (it's true). If you are worried about your rabbit try to keep the rabbit inside the house more and not in hutches that leave the rabbit outside.