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d/dr([pi*r^2)=2*pi*r.

Similarly, the derivative of the formula for the volume of a sphere is equal to the formula for surface area: d/dr(4/3*pi*r^3)=4*pi*r^2.

I'm positive that these are consequences of Stokes's (Green's) and Divergence theorems, but I don't know how to show this. Could someone please explain? Thanks.