It is a sector of a circle with radius LL and arc length cc. So the curved surface area of the cone is the area of the sector above. The area of a sector given the arc length cc and radius LL is given by A=\dfrac{1}{2}cLA=
2
1
cL. Now applying this to the cone, we have A=\frac{1}{2}cL,A=
2
1
cL, where LL is the slant height and cc is the circumference of the base. After some manipulations, A=\pi Lr,A=πLr, as given in the definition.
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Answer:
It is a sector of a circle with radius LL and arc length cc. So the curved surface area of the cone is the area of the sector above. The area of a sector given the arc length cc and radius LL is given by A=\dfrac{1}{2}cLA=
2
1
cL. Now applying this to the cone, we have A=\frac{1}{2}cL,A=
2
1
cL, where LL is the slant height and cc is the circumference of the base. After some manipulations, A=\pi Lr,A=πLr, as given in the definition.
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