Final answer:
The lateral surface area of a cylinder is calculated using the formula 2πrh, which cannot be directly solved with the options provided without specific measurements for radius and height. Dimensional consistency can be used to verify the correctness of various volume and area formulas for geometric shapes.
Step-by-step explanation:
The question asks to find the lateral surface area of a cylinder without providing specific dimensions, thus, it cannot be directly answered with the provided options (A, B, C, D). However, the lateral surface area formula for a cylinder is 2πrh, where 'r' is the radius and 'h' the height of the cylinder. The term 'lateral surface area' refers to the area of the curved surface of the cylinder, omitting the areas of the two bases.
To check the dimensional consistency of given formulas:
- V = πr²h is consistent since it combines a base area (πr²) and a height (h).
- A = 2πr² + 2πrh is also consistent as it represents the sum of the areas of the cylinder's two bases (2πr²) and its lateral surface (2πrh).
- V = 0.5bh is consistent for the volume of a pyramid or cone, not a cylinder.