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## Homework Statement

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.

## Homework Equations

SA= 4 pi r^2

r(0)=1.2

r(180)=1

## 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?