Hello All I could get some help I would greatly appreciate it. I am trying to figure how to calculate the dissolution time of sphere undergoing constant corrosion at a rate of corrosion. Through a little google-fu, I found an article which gives me the solution ( http://arxiv.org/pdf/1208.5925.pdf ) but I am having trouble understanding the proof. In this article there is a dissolving sphere From this article we know that the mass of the sphere is equal to dm/dt = -c*s(m) (1 and the general solution is m(t)=mo - A*(mo^2/3)*t + (1/3)*(A^2)*(mo^(1/3))*(t^2) -1/27*(A^3)*(t^3) or m(t) = (a-k*t)^3 a = initial mass = (mo)^1/3 k = (A/3). The article then gives an example where mo = initial mass = 10 grams p = density = 0.8 mg/mm^2 c = corrosion rate = -0.003 mg/(s*mm^2) I am having difficulty understanding how to relate the rate of corrosion c to A. I know that c = (dm/dt)/s(m) The article shows a series of graphs for Mass, Radius, SA, and Volume vs time. I copied these graphs into excel and add used excel to find a trendline. m(t) = -2E-07*t^3 + 0.0002*t^2 - 0.079t+ 9.9879 By plugging values into the trend line above I was able to find a solution to A = 0.0173. However, do not understand how to relate A to c(-0.003). Some help would be greatly appreciated.