Is there a relationship between the size of a cell and it's function

Yes, there is a relation between the size of a cell and it's function.

Explanation:

Cell generally remain small in size so that these have larger surface area.For example, lets imagine a cube with each of its sides measuring 2mm. The total surface area of this cube will be 2mm X 2mm X 6 = 24 sq.mm.Suppose we cut this cube into 8 small cubes, reducing each side to half of its length.Then the total surface area of these 8 cubes will be 1mmX1mmX 6(surfaces) X 8 = 48 sq. mm.This is double than that of the larger cube, but the volume of both the cube remains same.This larger surface area relative to volume of the cell ensures greater diffusion of substances and thus enhances cell functioning.

Ribonuclease activity is a type of nuclease that catalyzes the degradation of rna into small components.