We'd like to help, but unfortunately, there are so many variables here that it's a not really a question that is answerable in a meaningful way. Here's some questions you could ask back to the teacher.
What database platform?
How much header information per page? per row?
What's the database page size?
Is the data in the database page compressed? If so what kind/level of compression is being used?
How much space per file is taken up by system objects?
Also please tell your teacher that things like this will serve you 0 use in the real world. Bytes per page, per file sure. Number of pages (and records) per file sure. Figuring out the disk size based on the number of cylinders, nope totally useless. The computer will do that for you.
The time to read one record at random? That'll totally depend on where the head is at the time, where the record is at the time, if the record is in the buffer, if the record is in the disk cache, what else the disk is doing at the time (odds are it isn't handling just your request).
Sorry this answer isn't of much more help than giving you some smart ass responses for your teacher. But in reality you don't have enough information unless I'm going to start making a whole lot of assumptions.