Final answer:
The thin circular plate will cool the fastest due to its larger surface area compared to the cube and the sphere, facilitating greater heat dissipation.
Step-by-step explanation:
The object that will cool the fastest among a cube, a sphere, and a thin circular plate, all with the same mass and made of the same material, is the one with the greatest surface area exposed to the air. Cooling rate is influenced by the surface area since heat transfer occurs at the surface. A sphere has the smallest surface area for a given volume, whereas a plate, especially a thin one, has a much larger surface area. Thus, the thin circular plate will cool the fastest because it has more surface area exposed to the air which enhances heat dissipation.