Final answer:
The volume of the larger pyramid, when similar to a smaller pyramid with a known volume and given the ratio of their heights, is found by cubing the height ratio to get the volume ratio. Using the volume of the smaller pyramid and solving the proportion, we find the volume of the larger pyramid is approximately 1563 cubic meters.
Step-by-step explanation:
The student is asking about the volume of a similar pyramid given the volume of a smaller one and the ratio of their heights. When dealing with similar figures, the volumes are proportional to the cubes of the ratios of their corresponding dimensions.
In this case, the ratio of the heights is 2:5. Hence, we need to cube this ratio to obtain the ratio of the volumes. The cube of the ratio of the heights is 2³:5³, which simplifies to 8:125. Knowing that the volume of the smaller pyramid is 100 cubic meters, we calculate the volume of the larger pyramid by setting up a proportion:
8/125 = 100/Volume of larger pyramid
We solve this proportion to find the volume of the larger pyramid:
Volume of larger pyramid = (125/8) × 100
Calculating this, we get:
Volume of larger pyramid = 1562.5 cubic meters
Therefore, rounding to the nearest whole number, the volume of the larger pyramid is approximately 1563 cubic meters, which means none of the answer choices A, B, C, or D are correct.