Possible Duplicate:
Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
We all know that the volume of a sphere is:
$V = \frac{4}{3}\pi r^{3}$
and its surface area is
$S = 4 \pi r^2$
Now we see that
$\frac{dV}{dr} = S$
As well, the area of a circle is
$A = \pi r^2$
The circumference is
$C = 2 \pi r$
Now we see again that
$\frac{dA}{dr}=C$
There may be more that I have not noticed. Why does this relationship occur?