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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