I'm trying to prove that area of some solid figures (for example a cube and a sphere) can be found using its volume. To say it I take the solid, for example a cube, I've got it's volume: $ V_c = l^3 $ now I increment $l$ by $h \rightarrow 0$ and subtract the initial volume: $(l + h)^3 - l^3$. Dividing it by $h$ I: $ S_{c/2} = \frac{(l+h)^3-l^3}{h} = 3l^2 $ It works because I get only half-cube shell applying this method.
The same can be done with a sphere: $ V_s = \frac{4}{3}\pi r^3$ $ S_s = \frac{4}{3} \pi \frac{(r+h)^3- r^3}{h} = 4 \pi r^2$ it also works because I get a spheric shell.
How is it possible that the infinitesimal volume of the shell is also the expression of the area? In particular I can't explain the sense of dividing by $h$ to find the area?