An easy-to-assemble reamer for medical applications includes a shaft portion, a disposable tapered hollow reamer sleeve and a modular pilot. The shaft portion has a proximal end for attachment to a drill, a central cone element with one or more slots and a distal threaded end. The tapered hollow reamer sleeve has integrally attached one or more torque transmitting tabs at the larger end and a collet taper at the smaller end and slides over the shaft distal end engaging tabs with the slots. The modular pilot has a threaded central aperture engaging shaft thread and a collet taper mating with the collet taper of the reamer sleeve substantially coinciding their centerlines. The disposable hollow cutter sleeve has a plurality of cutting elements and apertures that discharge bone and bone cement debris into the space between the reamer and the shaft. With this construction, the reamer transmits reliable, wobble free, reaming torque in a highly efficient manner.