A shaping apparatus for shaping a flotation core includes a worktable. At least one support is adjustably mounted on the worktable to be adjustable at least along a z-axis and configured to support the core. At least one engagement mechanism is mounted on the worktable and is displaceable relative to the worktable to engage and retain the core in position on the worktable. A gantry supports a rotary shaping machine so that a tool of the machine rotates in a y-z plane. The worktable and the gantry are displaceable relative to each other along x-, y- and z-axes. A displacement mechanism displaces the worktable and the gantry relative to each other on receipt of suitable control signals.