Which tool performs the function of shaping a workpiece's outside surface?

The correct answer to the question about which tool shapes a workpiece's outside surface is the shell mill.

A shell mill is specifically designed to cut and shape the outer surfaces of a workpiece. It typically has multiple cutting edges and is mounted on a separate arbor, allowing for the efficient removal of material from the outer diameter of a workpiece. This capability is particularly useful for machining flat surfaces or creating grooves and contours on the exterior of components.

While a slab broach is primarily used for internal shaping and creating slots, and a single-point tool is usually employed in turning operations for creating features such as diameters or grooves along a workpiece's length, the face cutter is mainly used to mill flat surfaces. Each of these tools has specific applications, but the shell mill stands out for its effectiveness in machining the external features of workpieces.