What do you mean by cross range dimension of a radar's resolution cell?
Imagine the radar as a torch.  You hold it in your hand and point it at the floor.  The spot projected by the torch is the "resolution cell".  Point it near your feet and the cell is small, so the cross-range dimension of it is small.  Point it at the floor 20 feet away and the spot is elongated and long.  The cross-range dimension, in that case, is large.  So you get the same resolution (the resolution cell) in a larger space (the cross-range dimension) resulting in lower detail.