Final answer:
The statement is false. Two cylinders with equal volumes can have different surface areas.
Step-by-step explanation:
In general, the statement is false. The surface area of a cylinder depends on its height and radius, while the volume only depends on the radius and height. Therefore, it is possible for two cylinders to have the same volume but different surface areas.
For example, consider two cylinders with the same volume of 100 cubic units. The first cylinder has a radius of 5 units and a height of 4 units, while the second cylinder has a radius of 2 units and a height of 25 units. Both cylinders have a volume of 100 cubic units, but their surface areas are different. The first cylinder has a surface area of 286.48 square units, while the second cylinder has a surface area of 269.73 square units. Thus, their surface areas are not equal.