linear ODE problem 
A substance evaporates at a rate proportional to the exposed surface. If a spherical mothball of radius  $\frac{1}{2}$ cm has radius $0.4$ cm after $6$ months, how long will it take:

*

*For the radius to be  $\frac{1}{4}$ cm?


*For the volume of the mothball to be half of what it was originally?

So I understand the radius of the sphere gets smaller as the time goes by.
$$\frac{dV}{dt}=4\pi (r-t)^2$$
I came to this, but it does not seems to right

$$\frac{d}{dt}(\frac43\pi r^3) = -4k\pi r^2, $$
$$3r^2\frac43\pi \frac{dr}{dt} = -4k\pi r^2,$$ 
$$\frac{dr}{dt} = -k $$
