To determine which object— the small cube of iron or the large flat sheet of iron—will completely rust first, we need to consider the surface area-to-volume ratio of each object as well as the process of rust formation.
Rust (iron oxide) forms when iron reacts with oxygen and moisture in the environment. The rate of rusting is influenced by the surface area exposed to air and moisture.
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Surface Area: The flat sheet of iron has a much larger surface area compared to the small cube of iron, even though they both have the same volume. A larger surface area allows more iron to be exposed to the environment, facilitating a greater amount of rusting.
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Rust Formation: Rusting occurs at the surface of the iron. In the case of the cube, less of its material is exposed to the elements at any given time compared to the flat sheet. Thus, for a given volume of iron, the flat sheet will have a higher rate of rusting since more of its surface is available for the rusting reaction.
In conclusion, the large flat sheet of iron will rust completely before the small cube of iron due to its larger surface area, which allows more iron to be oxidized and exposed to oxygen and moisture simultaneously.