Offered a job but there's a big problem, please somebody help!

So my university has this area on the site where students can apply for jobs at the university to do while they're studying. I found this brilliant vacancy which was relevant to my degree and the career I want so applied for it and had an interview earlier today.

The interview went very well until at the end when I asked about how many hours the contract would be (I had actually emailed to ask this beforehand but didn't receive a reply). Basically, it turns out it would actually be full time (37 hours) even though it was definitely advertised as part time. I have just checked the job advert again and it definitely only says part time. I just got an email offering me the job but I really don't think I could cope with so many hours. I'm a full time student and only have classes 12 hours a week but there is a LOT of work to do outside of uni. I mean, would it even be possible to take this job? I'm so confused as to why they are advertising a full time vacancy exclusively to students at the uni (although it did say part time!), but I really do want this job and I have no idea what to say to them.

Just go back and ask them the question eg Thanks you very much for the job offer, I'd be very excited to do the job. However, the job advert said it was part-time, and as I am a full time student, I only feel able to work xx hours per week. Can you confirm that the role is part-time, as advertised, and that I could work hours compatible with my degree?

Ok I will do, thanks although do you have any idea why they would say it was full time in the interview?