Final Answer:
The volume of cylinder B is 40mm³.
Step-by-step explanation:
To find the volume of cylinder B, knowing that cylinders A and B are similar, we can use the ratio of their volumes. Since they're similar shapes, their volumes are proportional to the cube of their corresponding dimensions. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. As volumes are directly proportional to the cube of the dimensions, if the volume of cylinder A is 10mm³, the ratio of the volumes between A and B is 1:4 (since 10mm³ : x = 1 : 4, where x is the volume of cylinder B).
Now, using the ratio of 1:4, we can determine the volume of cylinder B. If cylinder A has a volume of 10mm³, cylinder B, being four times larger in volume due to their similarity, has a volume of 10mm³ * 4 = 40mm³.
Therefore, the volume of cylinder B is 40mm³. This demonstrates the concept of similarity in shapes where corresponding dimensions have a proportional relationship affecting their volumes. Applying the ratio between their volumes allowed us to find the volume of cylinder B using the known volume of cylinder A.