The total surface area of a cylinder of radius ' r ' and height ' h ' is

The cylinder's total surface area is calculated by adding the areas of the two bases and the curved surface.

As a result, the formula for the cylinder's total surface area is as follows:

Total cylinder surface area = area of two bases + area of the curved surface

Because the cylinder's bases are circular in shape, their combined area is $\pi r^2+\pi r^2$

We already know that a cylinder's curved surface area is 2rh.

Total surface area of cylinder $=\left(\pi r^2+\pi r^2\right)+2\pi rh$

$=2\pi r^2+2\pi rh$

Total surface area of cylinder $=2\pi r(r+h)$