Question

We know that the volume and surface area of sphere is \(V = \dfrac{4 \pi r^3}{3}\) and \(S = 4 \pi r^2\). But I notice that \(\dfrac{\text{d}V}{\text{d}r} = S\).

Coincidence or is there some special reason for this?

Answer 1

@hartnn @Hero @ash2326 @Copythat @NickR @satellite73 @mahmit2012

Answer 2

http://www.pleacher.com/mp/mlessons/calculus/relderiv.html