How does a cells ratio of surface area to volume change as the cell grows larger?
Assuming that the shape of the cell stays the same, if the cell increases it's linear dimension (length) by a factor of 2, the surface area will be increased by a factor of 4, and the volume will be increased by a factor of 8. You can verify that this is true with simple shapes such as spheres or cuboids.
The volume grows more rapidly than the surface area. Hence the surface area to volume ratio decreases.