Differentiation of a sphere -- raindrop evaporating as it falls

[moonwzrd]

< Moderator Note -- Thread moved from the technical PF Calculus forum >[/color]

I can't seem to grasp the idea of this problem, any help is much needed. The problem reads, "As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that is proportional to its surface area (S=4πr^2). Show that the radius decreases at a constant rate.

 

[rock.freak667]

The problem says that the drop "begins to evaporate at a rate that is proportional to its surface area". This means that the volume is decreasing with time proportionally to its surface area S.

Can you write out this proportionality in terms of S?

They are asking you to find the rate at which the radius is changing. This means that they want you to find dr/dt. How can you use the chain rule and the proportionality you wrote out above to get dr/dt?