I'll do a Physics thing:

Assume a spherical snowball. Then the surface area of the snowball is

SA = 4(pi)r^2 = (pi)x^2 (where x is the diameter)

(Note: I'm avoiding d as the diameter because otherwise I'd be taking a "dd/dt" which is confusing!)

So

d(SA)/dt = 2(pi)x * dx/dt

1 cm^2/min = 2(pi)(10 cm) * dx/dt

Now solve for dx/dt.

-Dan