A spherical mothball of original radius 1.2 cm slowly
evaporates such that 180 days later, its radius is only 1 cm.
Physically, the rate of evaporation dr/dt is proportional to the
surface area of the sphere. Determine a) the time required for
the radius of a new mothball to shrink to 25 percent of its
original radius, and b) the time required for the volume of a
new mothball to become half of its original value.
SA= 4 pi r^2
The Attempt at a Solution
I started by saying -dr/dt = c1 4 pi r^2
where c1 is a constant of proportionality
Then through separation of variables I found that
1/r = 4 pi c1 t + c2
after imposing the initial conditions I found c1=7.383*10^-5 and c2=.833
so I have
1/r = 4 pi (7.383*10^-5) t + .833
and this gives me answers of
1) 2694 yr
2) 233.82 yr
but these aren't right. Any ideas of where I went wrong?