Final answer:
The ratios of the heights, base areas, and volumes for the two similar pyramids with heights of 5 m and 15 m are 1:3, 1:9, and 1:27, respectively.
Step-by-step explanation:
The question involves calculating the ratios of the heights, base areas, and volumes of two similar pyramids. For similar figures, these ratios are based on the scale factors between the corresponding dimensions of the figures. In the given problem, Pyramid B is smaller than Pyramid A, with a height of 5 m for Pyramid B as compared to 15 m for Pyramid A. The ratio of the heights is therefore 5 m to 15 m, which simplifies to 1:3.
When dealing with areas, the scale factor needs to be squared, so the ratio of the base areas is the square of the height ratio, which would be (1:3)^2 or 1:9. For volumes, the scale factor is cubed, so the ratio of the volumes would be (1:3)^3 or 1:27.