Final answer:
To build the largest volume pyramid from an 8-inch by 8-inch piece of paper, use the entire paper to make the square base, which corresponds to option (b). This maximizes the base area and allows for the greatest potential volume according to the volume formula for a square-based pyramid.
Step-by-step explanation:
To build a pyramid with a square base with the greatest volume from an 8-inch by 8-inch piece of paper, you would want to create a pyramid with a base as large as possible. This means you should use the entire sheet of paper for the base, which addresses option (b) from the student's question. By maximizing the area of the square base, you are maximizing the potential volume of the pyramid. A cube or a triangular pyramid would not make efficient use of the entire paper for just the base, and thereby, those options would not result in the greatest volume.
The volume of a square-based pyramid is given by the formula V = (1/3)·base area·height, where the base area is the side length squared for a square base. In this case, using the whole paper maximizes the base area and subsequently allows for the greatest potential volume, assuming you could achieve the optimal height.