One of the main attractions of a "study Bible" is the mini-commentary of its footnotes. Scholars gather explanatory material, important cross-references, key observations, and answers to readers' likely questions. One-volume commentaries and larger commentaries on whole books of the Bible offer much more background to guide readers. This project is meant to give you practice using these kinds of resources.
Use commentaries to investigate the cultural/historical background of a passage in 1 or 2 Corinthians as if you were preparing to lead a Bible study or Sunday school class on that passage. The idea is not that you would 'teach the commentaries' or focus on the background, but that you would learn the background and draw on it to make you a more effective interpreter and teacher of the passage.
Choose a common passage from 1 or 2 Corinthians that typical commentaries treat as a whole unit. Aim for a length of about 10-20 verses.
Read the passage closely, collecting observations and questions. Do the requisite research in at least one scholarly single-volume commentary and one whole-book scholarly commentary. You will find these in the library. Internet sources are not acceptable as they vary so widely in quality. The footnotes in a study Bible are not adequate (though you can of course read them). As you work through the passage using those sources, develop a list of points you would want to emphasize in your own teaching of that passage in a Bible study context. Use footnotes for (a) me to see how the background helps you understand those points, and (b) you to supply references if people in your Bible study are curious or skeptical and want to know more.
You will find that commentaries are of uneven quality. Some just rephrase the text, which is of little help since you should be able to do that yourself. Others crowd out the voice of the biblical author: they may lead readers in unproductive directions away from the text, stifle their own investigations of the passage by providing interpretive answers too easily and overconfidently, or misuse the scarce space they have by emphasizing less important things. Good commentaries offer the right resources to draw readers efficiently, actively, and fruitfully into a passage.
I don't have a formal length requirement, but if you need one, I suggest about a thousand words. Follow the directions in my handout for writing papers. Remember, I want to see proper style, clear writing, a thorough answer to the question, and explicit citations of course materials. Of course, cite any sources you draw on, whether directly or indirectly, or you're plagiarizing.