### 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.

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.

$$\text{The lateral (or curved) surface area of a cylinder}$$ $$=$$ $$\text{Area}$$ $$2$$ $$=$$ $$2\pi rh$$