Total surface area of a cylinder having base radius “$r$” and height “$h$” is equal to

Concept: Total surface area of a cylinder = curved surface area $+ 2\times$area of the circular base.

If we unfold the cylinder in the given figure, the area of the rectangle equals the curved surface area of a cylinder.

Here, one side of the rectangle is equal to " $h$ " and the other side is equal to perimeter of circular edge of the cylinder, i.e., "$2\pi r$".

Now, the curved surface area of the cylinder $=2\pi rh$

Area of circular base $=\pi r^2$

Now, total surface area of a cylinder = curved surface area $+ 2\times$area of the circular base $=2\pi rh+2\pi r^2$

Hence, the total surface area of a cylinder is $2\pi rh+2\pi r^2$.