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!)
d(SA)/dt = 2(pi)x * dx/dt
1 cm^2/min = 2(pi)(10 cm) * dx/dt
Now solve for dx/dt.