How would you explain to a friend , the process for finding the total surface area of a cylinder using the net of a cylinder?

The toal surface area of a cylinder is 2πrh+2πr²

Step-by-step explanation:

The "net" of any geometrical shape refers to the two-dimensional equivalents of the three-dimensional object.  

e.g. geometrical net of a cylinder would consist of two circles (one each at top and bottom) and a rectangle extending from bottom to the top in a curvilinear manner.

Hence, the Total surface area (TSA) of the cylinder can be found

by considering cylinder to be made of three parts

The surface area of a circle (for 2-dimensional figures surface area is the same as area since the thickness factor is 1)= πr²

Since there are two circles= surface area (combined)= 2πr²

Moreover, this circle extends to height h. Hence, the combined surface area of the circle extending to height h (int he forms of the tube)= circumference*height= 2πrh

hence TSA= 2πrh+ 2πr²