Final answer:
The ratio of the volumes of two similar cylinders, with a ratio of their edge lengths being 4:3, is calculated by cubing the linear ratio, which results in a volume ratio of 64:27.
Step-by-step explanation:
The question involves finding the ratio of the volumes of two similar cylinders when the ratio of the lengths of their edges is 4:3. To find the ratio of the volumes, we need to use the fact that the volume of a cylinder (V) is the cross-sectional area (A, which is the area of the base circle) times the height (h), given by the formula V = πr²h.
For similar figures, the volumes are proportional to the cube of the ratio of their corresponding linear dimensions. Since the cylinders are similar and the ratio of their edges is 4:3, we cube this ratio to find the ratio of their volumes.
(4/3)³ = 64/27. Therefore, the ratio of their volumes is 64:27.