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 circle at the bottom the circular tube which extends for height "h" of the cylinder the circle at the top (considering it is closed cylinder)

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