Cone side surface area

We enter a regular n-angle pyramid into the cone. The area of ​​the side surface.



where Pn is the perimeter of the base of the pyramid, and ln is the apothem.
With an unlimited increase in n, the base perimeter Pn unboundedly approaches the length C of the circumference of the base of the cone, and the apothem ln - to the length l of the generator. Accordingly, the lateral surface of the pyramid approaches indefinitely 0.5Cl. In this regard, the value 0.5Cl is taken as the area of ​​the side surface of the cone.
The area of ​​the side surface of the cone is calculated by the formula



where R is the radius of the base of the cone, and l is the length of the generator.
For the side surface area of ​​a truncated cone with radii of bases R1, R2 and forming l, the formula is obtained