Final answer:
The volume of the larger solid is obtained by finding the cube of the surface area ratio multiplied by the smaller solid's volume. The specific steps involve calculating the square and cube of ratios and applying them to the known volume.
Step-by-step explanation:
The question asks about finding the volume of a larger solid given the surface areas and volume of a similar smaller solid. We use the property of similar solids, which states that the ratio of the areas is the square of the ratio of the lengths, and the ratio of the volumes is the cube of the ratio of the lengths. In this case, we first find the ratio of the surface areas:
- Surface area of smaller solid: 726 yd²
- Surface area of larger solid: 1,014 yd²
The ratio is √(1014/726), which, when cubed, gives us the ratio of the volumes. Then we multiply this ratio by the volume of the smaller solid to find the volume of the larger solid. The calculation, when rounded to the nearest hundredth, gives an answer which should match one of the options provided.