A detailed theoretical qualitative, as well as quantitative, analysis of the influence of the dimensions of Bi(2223)/Ag based cylindrical magnets on the energy stored in the magnet's winding was performed for various operating temperatures. The results achieved can be used to consider the potential suitability of the high-temperature superconductivity magnets for the purposes of micro-superconducting magnetic energy storage applications. A mathematical model which enables one to calculate the values of basic parameters, such as the critical current and stored energy of cylindrical magnets consisting of the set of Bi(2223)/Ag pancake coils, was developed with respect to the real distribution of the magnetic field in the winding and the angular dependence (anisotropy) of the Ic(B) characteristic of the tape. An example of a detailed analysis of the influence of the winding geometry, which is changed within the same overall length of 1, 2 and 5 km of the multifilamentary Bi(2223)/Ag tape, was performed at the temperatures of 77, 65 and 4.2 K. The most interesting and important result achieved is that the geometry of the winding that corresponds to the maximum stored energy differs according to the temperature. The disc-shaped magnets, which consist of a very low number of pancake coils, are the most suitable solution at 77 and 65 K. Simultaneously, the value of the stored energy is practically independent of the bore diameter of the magnet. On the other hand, when looking for the optimum winding geometry at 4.2 K, the magnets with the smallest bore diameter are more suitable, while the value of the energy stored does not depend on the number of pancake coils.