Final Answer:
C. 192π units² because Option C is correct because it accurately combines the lateral surface area and the area of the circular bases for the given right cylinder.
Step-by-step explanation:
The surface area of a right cylinder is given by the formula \(2πr^2 + 2πrh\), where \(r\) is the radius of the base and \(h\) is the height. In this case, we need to consider both the lateral surface area (\(2πrh\)) and the area of the two circular bases (\(2πr^2\)).
Comparing the options with the formula, we find that \(2πr^2\) is common in all options, and the only differing factor is the lateral surface area. The correct answer must be the one that provides the correct lateral surface area for the given cylinder.
Now, the lateral surface area of a cylinder with radius \(r\) and height \(h\) is \(2πrh\). Looking at the options, we find that only option C (192π units²) provides the correct lateral surface area.
Therefore, the correct answer is option C (192π units²) as it correctly combines the lateral surface area and the area of the circular bases for the given right cylinder.
In summary, the surface area of the right cylinder is the sum of the lateral surface area and the area of the circular bases, and option C is the only one among the choices that satisfies this requirement, making it the correct answer.
Therefore, the correct answer is option C