As long as human population continues to grow, the world will get full. Let's not argue here about how long that might take.
When I say get full, I mean we will reach a point where more can't be supported. I bet we'd reach a point long before then when the quality of life was so reduced that it wasn't fun to be alive any more.
If you took the current world population and put it in Rhode Island (never mind how), each person would have (assuming you bulldozed Rhode Island flat and filled in all the holes first) a square of land less than two feet on a side. Sort of like a colossal crowded elevator.
A current resident of Greater New York City, by comparison, has about 400 square feet--twenty feet on a side--to himself. Again, supposing you bulldozed Greater New York.
To accommodate the entire world population at that density would take all of New York, New Jersey, and most of Pennsylvania.
How much agricultural land would it take to feed and clothe all of them? Well, roughly speaking, all that's currently under cultivation.