The constant of proportionality is k > 0, v is the volume, s is the surface area. remember that you must use the prime notation for derivatives, not the leibniz notation, in all of your answers. a raindrop evaporates at a rate that is proportional to the surface area, write this as a differential equation: equation editorequation editor=0.since v=43πr3 we have by the chain rule that dvdt=v′=equation editorequation editor. substituting this into the original differential equation, along with the equation s=4πr2, and solving for r′ we find that