A cylinder has two plane ends. Each plane end is circular, and these two plane ends are parallel to each other.
Also, a cylinder has two dimensions, namely radius and height.
The net of a cylinder looks like this.
\(\text{The total surface area of a cylinder}\) \(=\) \(\text{Area}\) \(1\) \(+\) \(\text{Area}\) \(2\) \(+\) \(\text{Area}\) \(3\)
\(= \pi r^2 + 2\pi rh + \pi r^2\)
[Since \(\text{Area}\) \(1\) and \(\text{Area}\) \(3\) are circles]
\(= 2\pi r^2 + 2\pi rh\)
\(= 2\pi r(r + h)\)
Let us now look at the lateral surface of the cylinder.
The shaded portion forms the lateral surface of the cylinder.
\(\text{The lateral (or curved) surface area of a cylinder}\) \(=\) \(\text{Area}\) \(2\) \(=\) \(2\pi rh\)