Problem 1. Spherical pellet in a spherical tank. In class, we considered the time-varying PDE model of the spherical pellet suspended in a spherical tank where there is a zero-order reaction consuming the solute dissolving from the pellet. We can assume a pseudo steady state, which is not quite at steady state but the changes are occurring so slow that for all practical purposes the dissolution rate is equal to the rate of consumption. Further, note that the pellet is going to shrink with time but if we assume it does so very slowly, we can assume that at pseudo steady state, the pellet radius is constant. Pseudo steady states are useful approximations in modeling chemical and biological processes. Derive the concentration profile in the tank at pseudo steady state. Hint: You will have to integrate twice!