Net of a Cone
Cone Net
See how a 3D cone unfolds into its flat net - a sector and a circle.
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Surface Area of Cone
Surface Area of Cone

Take a cone made from a paper. Cut it as its slant surface and open it as shown in the Figure. Now, the curved surface of cone is transferred to the flat form as shown in the Figure, which is a sector. And the length of this sector is equal to the circumference of the circular base of the cone.

l l 2πr
Figure (i)

Now, cut the sector into 4 equal pieces as shown in the Figure (ii) and color two pieces with red.

Then, arrange two small sectors in the same directions and remaining two in opposite directions as shown in figure (iii).

l πr πr
Figure (iii)

Here,
If the radius of base of the cone is 'r', slant height is 'ℓ' and the vertical height is 'h', then,

Curved Surface Area (CSA) Derivation
Curved surface area of the cone (CSA) = Area of parallelogram
= base × height (Note: The parallelogram base is half the original arc length)
= πr × ℓ
= πrℓ sq. unit
Total Surface Area (TSA)

Total surface area of the cone (TSA) = Area of base + Curved surface area (CSA)

Total surface area (TSA) = πr² + πrℓ

Total surface area (TSA) = πr(r + ℓ) sq. unit

Solve Questions — Cone Calculator
CSA = πrl  |  TSA = πr(l+r)  |  l = √(r²+h²)