Final answer:
Each of the four shapes created from four unit cubes can be used to construct a 2×4×4 cuboid as eight copies of a single shape will equate to the volume of the cuboid, which is 32 unit cubes. However, fit and orientation must also be considered to ensure they can form the cuboid without gaps or overlapping.
Step-by-step explanation:
The student's question involves ascertaining which of the four shapes constructed from unit cubes can be used to make a 2×4×4 cuboid when eight copies of the shape are put together. This question requires an understanding of how shapes can be combined to fill up space without leaving any gaps or overlaps. It is essential to remember that the volume of the cuboid, which is 32 unit cubes (2×4×4), must be equal to the volume of the eight shapes combined.
Each shape is made from four unit cubes. Consequently, if we take eight copies of one shape, we would have a total volume of 32 unit cubes (8 copies × 4 unit cubes per copy). This matches the volume required to build the 2×4×4 cuboid. Therefore, each of the shapes can be combined to form a 2×4×4 cuboid.
However, the question implied that more than one shape might not be able to make a cuboid of that size. This means we would need to consider the shapes' fit and orientation to form the larger cuboid without gaps. All shapes that can fit together neatly without leaving gaps or overlapping can form the intended cuboid.