The constant of proportionality is k, V is the volume, S is the surface area. Remember that you must use the prime notation for derivatives, not the Leibniz notation, in your answers.
A raindrop evaporates at a rate that is proportional to the surface area:
.
Since and we have by the chain rule that
. Substituting into the original differential equation and solving we find that
so that
You can earn partial credit on this problem.