Consider the process of the melting of a spherical ball of ice originally at $$0^\circ\text{C}$$. Assuming that the heat is being absorbed uniformly through the surface and the rate of absorption is proportional to the instantaneous surface area. Which of the following is true for the radius $$r$$ of the ice ball at any instant of time? Assume that the initial radius of the ice ball at $$t = 0$$ is $$r = R_0$$ and that the shape of the ball always remains spherical during melting. Also assume that $$L$$ and $$\rho$$ are respectively the latent heat and density of ice at $$0^\circ\text{C}$$.