I'm a first year PhD in Computer Science at a UK university. Recently, my supervisor has asked me to join a funded research project consisting of other post-docs and lecturers, i.e. I'll be the only PhD student in that project. My supervisor believes that it will be helpful for me to join since my research topic and a project's theme have many similarities, which I also agree. However, he doesn't mention anything about if I get paid to work in that project. So, I wonder if it is normal for a PhD student to work in a funded research project without getting paid.
I'm not in the U.K., but in my part of the world, it's common (one might say usual) for computer science PhD students to be paid. Is the determination of whether a PhD student is paid related to whether the project is funded? Not necessarily.
When is it appropriate to ask about payment?
Should you talk to your supervisor about this? Instead of asking
Is it normal to not be paid?
Is it unusual to be paid?
In any scenario in which is is not unusual to be paid, it is neither inappropriate nor offensive to (politely) ask whether you can be paid for work you are doing.* In your case, it is definitely appropriate. So, go ahead and talk to your supervisor about this.
* Here is an example of a scenario where it is not usual to be paid, and it was therefore inappropriate to ask for payment. As you can see, it's an extreme example :)