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
`\frac43\pi r^3` and surface area
`4\pi r^2`. So

`(\mathrm dV)/(\mathrm dt)=4\pi r^2k`