Why does the volume of a cell reduce faster than surface area?

The volume is typically dependent on the cube of cell's dimension, while the surface area is dependent on the square of cell's dimension. That is,

Volume `alpha`  (dimension)^3

Surface area `alpha`  (dimension)^2

If we assume the cell to be spherical in shape, with a radius of "r", then the volume is given as 4/3 `pi`r^3 and the surface area is given as 4`pi`r^2.

Thus, volume is more dependent on the dimension as compared to the surface area.

For illustration, if the radius of the cell halves, then the volume reduces by a factor of 8 (it would be 1/8th original value), while the surface area would reduce by a factor of 4 (it would be 1/4 th of its original value).

Hence, the volume reduces faster than the surface area of the cell. It also means that the volume increases faster than the surface area of cell.

Hope this helps.