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.
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