"They listen to the radio in the evening."
Translation:Вони слухають радіо увечері.
It could be "in" or "at" most of the ties, or even "on" sometimes.
У кишені - in the pocket
У школі - at the school
У списку - on the list
"У" in this sentence indeed means "in". As articles are not found in Ukrainian in the most cases they aren't even translated.
I cannot tell you if it is etymologically correct, but it looks very logical.
For us слухати is a verb that just takes a noun directly. To compare, In English you have to say "listen to something" and not directly "feed" the noun to the verb, but "see something" and not "see to something" or "see at something". In Ukrainian "listen" works the way "see" works in English rather than "listen"
So, слухати takes a clean noun without prepositions.
Вони слухають радіо/музику/мене/лекцію/маму/...