Final answer:
The volume of a model Egyptian pyramid with a square base 3 inches wide, assuming the pyramid is twice as wide as it is tall, is 4.5 cubic inches, corresponding to option (a).
Step-by-step explanation:
The Egyptian pyramids are popular for their grand scale and precise architecture, which often follows a ratio where the base is twice as wide as the pyramid is tall. To calculate the volume of a model pyramid with a square base, we can use the formula for the volume of a pyramid: V = (1/3) × base area × height. If the model pyramid has a base width of 3 inches, and assuming the proportions of the actual pyramids (where the base is twice the width of the height), we have a height of 1.5 inches because it is half of the width.
The base area of the pyramid would then be the width squared, which is 3 in. × 3 in. = 9 in.². Plugging these values into the volume formula, we get V = (1/3) × 9 in.² × 1.5 in. = 4.5 in.³. Therefore, the correct answer to the student's question would be 4.5, which corresponds to option (a).