“Ream of paper” is the correct phrase in English. A ream of paper is a quantity of sheets of paper that are the same size. A “rim of paper” sounds similar but is incorrect and not common in English.
Ream (Meaning and Use)
A ream of paper is a large quantity usually used with printers. When you have a printer, you need to have many sheets of paper that are all the same size.
For this reason, we have the sizes A4, A3, A2, etc. All of these sizes of paper usually come in a pack of 500 pages so that you make a lot of copies.
These packs of paper are called reams of paper. Reams of paper also means “any large quantity of paper”
We need to buy 50 reams of paper for the office.
We need reams and reams of paper.
Rim (Meaning and Use)
The rim is the circular outer edge of an object. Think about the top of a bottle. the rim is the part that you use to drink.
A rim of paper is not a common expression in English.
Your tire rims are falling off, you need new ones.
The rim of my glass has a salty taste.