For a school science project, Alice made a certain number of identical rocket prototypes comprising a cylindrical body for the fuselage, extending up to a height of 10 centimeters, and a conical nose cone representing the rocket's tip. If a total of 2,772 square centimeters of metal sheet was used in constructing all the rockets for the science project, with the base diameters of both the cylinder and the cone being 7 centimeters, and the slant height of the conical part being 8 centimeters, how many rockets did Alice make for the project?