Final answer:
Two cylinders are similar if the ratio of their corresponding linear dimensions is equal. The cylinders in question have different ratios for their dimensions, and therefore they are not similar.
Step-by-step explanation:
The question pertains to the concept of similarity between two geometric figures, specifically cylinders. Two figures are considered similar if they have the same shape, which means their corresponding angles are equal and the lengths of corresponding sides are proportional. The fact that the two cylinders may have different volumes or bases does not determine their similarity. Instead, similarity is based on the proportionality of their dimensions.
For the cylinders to be similar, the ratio of corresponding linear dimensions, such as radius to radius and height to height, should be the same. In the provided example, we have one cylinder with a radius of 25 cm and height of 35 cm, and another with a radius of 30 cm and height of 40 cm. The ratio of their radii is 25 cm / 30 cm = 5/6 and the ratio of their heights is 35 cm / 40 cm = 7/8. Since the ratios of corresponding dimensions (5/6 for radii and 7/8 for heights) are not equal, the cylinders are not similar.