Volume of a Spherical Raindrop: Differential Equation Solution

[Jamin2112]

Homework Statement

A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time.

Homework Equations

V = (4/3)πr³
S=4πr²

The Attempt at a Solution

dV/dt = -k(4πr²), k>0

Therefore dV/dt = -k(3/r)V

But the answer in the back of the book is

-kV^2/3

How did they get that?

 

[issacnewton]

in your solution, write r in terms of V and then absorb other constants in k.