The surface area of ​​the cylinder

We enter a regular n-angle prism into the cylinder. The lateral surface area of ​​this prism is Sn = PnH, where Pn is the perimeter of the base of the prism, and H is its height.
With an unlimited increase in n, the perimeter Pn approaches without limit the length C of the circumference of the cylinder base. Consequently, the lateral surface area of ​​the prism is unboundedly approaching CH. Therefore, the value of CH is taken as the side surface area of ​​the cylinder.
The area of ​​the side surface of the cylinder is calculated by the formula



where R is the radius of the cylinder, and H is its height.