A spherical rain drop evaporates at a rate proportional to its surface area at any instant `tdot` The differential equation giving the rate of change of the radius of the rain drop is _____

Explanation

We have given,

`(dV)/(dt) alpha S`

`implies(dV)/(dt)=−kS`, where `k`>`0`

`impliesd/dt[(4/3)pir^3]=−k(4pir^2)`

`implies4/3pi⋅3r^2((dr)/(dt))=−k(4pir^2)`

Therefore`(dr)/(dt)=−k`