When an object gets larger, why does the volume of an object increase faster than the surface area?

Let us consider the object to be a cell.

Explanation:

As a cell grows bigger, its internal volume enlarges and the cell membrane expands. This results in the increase in volume more rapidly than does the surface area, and so the relative amount of surface area available to pass materials to a unit volume of the cell steadily decreases. This means the surface area to the volume ratio gets smaller as the cell gets larger.

Example of a cube:

Cube size Surface area Volume

2cm 2 * 2 * 6 = 24 cm² 2 * 2 * 2 = 8 cm³

4 cm 4 * 4 * 6 = 96 cm² 4 * 4 * 4 = 64 cm³

6 cm 6 * 6 * 6 = 216 cm² 6 * 6 * 6 = 216 cm³

8 cm 8 * 8 * 6 = 384 cm² 8 * 8 * 8 = 512 cm³

This shows as the object gets larger, the volume of an object increases faster than the surface area.