Final answer:
The second square pyramid's volume, with base sides twice the length of the first pyramid, is four times greater than the volume of the first pyramid when calculated using the volume formula V = \frac{1}{3}Bh.
Step-by-step explanation:
The question asks about the comparison in volumes of two square pyramids given that the length of the side of the base of the second pyramid is double that of the first pyramid. Using the volume formula for a pyramid, V = \frac{1}{3}Bh, where B is the base area and h is the height, we can deduce the relationship between the volumes of the two pyramids.
Let's assume the side of the base of the first pyramid is L, and thus, the base area is L². The second pyramid has a base side length of 2L, making its base area (2L)² = 4L². Assuming the height remains constant for both pyramids, the volume of the second pyramid, V2, is:
V2 = \frac{1}{3}×4L²×h = \frac{4}{3}L²×h
The volume of the first pyramid, V1, is:
V1 = \frac{1}{3}L²×h
The ratio of the volumes is then:
V2 / V1 = (\frac{4}{3}L²×h) / (\frac{1}{3}L²×h) = 4
Therefore, the volume of the second pyramid is four times the volume of the first pyramid.