A growing raindrop. Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate.

Explanation

Let the constant of proportionality be k.
`rArr " " (dV)/(dt)=kA`
`V=(4)/(3)pir^(3) and A=4pi r^(2)`
`:. " " (d)/(dt) ((4)/(3)pir^(3))=k(4 pi r^(2))`
`:. " " 4 pi r^(2)(dr)/(dt)-k.4pi r^(2)`
`:. " " (dr)/(dt)=k="constant"`