Covering by Dismembered Convex Discs

Let us consider a great number of convex discs not "too different" from one another about which, apart from their total area, no further data are known. What can be said about the area of the largest square (or any other domain of given shape) which can be covered with the aid of these discs if we are allowed to cut each of them into a given number of suitable pieces? Analogously, we can raise the problem of estimating the area of the smallest square into which the pieces of the discs can be placed without overlapping if each disc is allowed to be cut into a given number of convenient pieces. These are; roughly expressed, the problems we intend to deal with in the present note.