What is the formula for calculating the lateral surface area of a cylinder?

The lateral surface area of a cylinder refers to the area of the curved surface that connects the top and bottom circular bases. To calculate this area, we can visualize the cylinder as a rectangle when it is "unrolled." The height of that rectangle corresponds to the height of the cylinder, and the width is determined by the circumference of the circular base.

The circumference of the circular base is given by (2\pi r), where (r) is the radius of the base. Therefore, when we multiply the circumference (the width of our rectangle) by the height (h) of the cylinder, we can derive the formula for the lateral surface area as follows:

[ \text{Lateral Surface Area} = \text{Circumference} \times \text{Height} = (2\pi r)h ]

Thus, simplifying that expression gives:

[ \text{Lateral Surface Area} = 2\pi rh ]

This correctly identifies the lateral surface area of a cylinder. Options focused on surface areas that apply to other geometric figures or the complete surface area of the cylinder, but they do not specifically represent the lateral surface area. Understanding this concept helps clarify the unique aspects of the