Theory:

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.
 
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The net of a cylinder looks like this.
 
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\(\text{The total surface area of a cylinder}\) \(=\) \(\text{Area}\) \(1\) \(+\) \(\text{Area}\) \(2\) \(+\) \(\text{Area}\) \(3\)
 
\(= \pi r^2 + 2\pi rh + \pi r^2\)
 
[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.
 
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The shaded portion forms the lateral surface of the cylinder.
 
\(\text{The lateral (or curved) surface area of a cylinder}\) \(=\) \(\text{Area}\) \(2\) \(=\) \(2\pi rh\)