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