"Why is there a radish in my spaghetti?"
Translation:Mengapa ada lobak di spageti saya.
Yes the root is "Apa" which is an interrogative pronoun. Mengapa is the formal version of "Why" and the slightly less formal and commonly heard version is "Kenapa" = why. From there it goes downhill quickly and you get a lot of really colloquial versions of it depending on what neighborhood of Jakarta you are in. Stuff like "Ngapa" "Gapaah" and my personal favorite "Ngapain apa" (what are you doing? very colloquial)
I think they are looking for the "ada" component, I wonder if "Kenapa spagetiku (itu/ini) berlobak?" would be right. Stylistically I think your "Why is my spaghetti with radish?" while accurate is a little awkward sounding.
In this question they are looking for "presence/absence" & "location" which really requires "ada" and "di", to express why there "is" something "in" something else. Versus "dengan" "with".