The exact question is: "Expanding peat discs are used to grow seedlings (google for an image!). These discs absorb water through their surface, causing an increase in height, h, while keeping a constant radius, r. Assume the disc is a cylinder and that the density of the disk, p = mass/volume, remains constant.
The rate of increase in the mass of the disc, m, is proportional to its total surface area. Derive a differential equation for the rate of change in m. You may include arbitrary constants, but the RHS should depend only on constants and m."
So far, I've thought of the fact that the mass only depends on the height, since the radius and density are constant. But then it mentions that the mass is proportional to the total surface area, meaning its proportional to height, since radius is constant and surface area depends on r and h.
The question says that the RHS should only depend on m, so does that mean that I have to define dm/dh in terms of m and constants? Or can I include h since it is the independant variable.
Those are my thoughts. I cannot seem to think of a DE for this aside from dm/dt = constant, unless, since dm/dt is directly proportional to surface area, it becomes dm/dt = constant + other_constant*h, as that is the surface area of a cylinder. But my thoughts on that answer is that the RHS does not contain m.