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

(a) For the radius to be $\displaystyle \frac{1}{4}$ cm?

(b) For the volume of the mothball to be half of what it was originally?