Final answer:
The scale factor is 125. The ratio of the areas is 15625:1. The ratio of the volumes is 1953125:1.
Step-by-step explanation:
The ratio of the volume of two similar solids can be determined using the scale factor. The scale factor is the ratio of the corresponding side lengths of the two solids. Let's call the scale factor 'k'. In this case, the volume ratio is 9000 in³ : 72 in³. To find the scale factor, we divide the larger volume by the smaller volume: k = 9000/72 = 125.
The ratio of the areas of two similar solids is equal to the square of the scale factor. In this case, the area ratio is (125)² = 15625 : 1.
The ratio of the volumes of two similar solids is equal to the cube of the scale factor. In this case, the volume ratio is (125)³ = 1953125 : 1.