When the curved surface of a right circular cone is cut along a slant edge and flattened, it forms a

Question

When the curved surface of a right circular cone is cut along a slant edge and flattened, it forms a circular sector.

To find the area of the curved surface area of a cone, we divide the sector into 20 smaller sectors and arrange them to form the shape as below. In fact, we can use more than 20 smaller sectors.

As shown in the GeoGebra app, as the number of sectors is increased indefinitely, then the shape will become a parallelogram.

Thus, the area of this parallelogram is $\pi r\times l$.

Curved Surface Area of Cone = $\pi rl$

Total Surface Area of Cone = Curved Surface Area + Circular Base Area
= $\pi rl$ + $\pi {{r}^{2}}$

Accepted Answer

Curved surface area: $\pi rl$ Total surface area: $\pi rl+\pi r^2$

Curved Surface Area of Cone

Curved Surface Area of Cone

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