Question

A spherical raindrop evaporates at a rate proportional to its surface area with (positive) constant of proportionality k ; i.E. The rate of change of the volume exactly equals ?k times the surface area. Write differential equations for each of the quantities below as a function of time.

Answer 1

A sphere of radius $r$ has volume $\dfrac43\pi r^3$ and surface area $4\pi r^2$. So

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2k$