I don't know why I even think about things like this, but...
If you take a hypothetical homogeneous bar of soap that's 3" X 2" X 1", it has a volume of 6 cu. in. and a surface area of 22 sq. in. If you wear off 1/4" all the way around, you now have a bar that's 2.5" X 1.5" X .5", with a volume of 1.875 cu. in. and a surface area of 11.5 sq. in.
Soooo, a relatively small reduction in outside dimensions (17%, 25%, and 50%, respectively) results in a huge reduction in both volume (69%) and surface area (48%).
I think it's time to go back to my Star Trek convention now...