Radian Measure: Show Cone Surface Area is $\pi rl$

[Sherlock16]

A cone with base radius $r$, vertical height $h$ and slant height $l$ has its curved surface slit and flattened out into a sector with radius $l$ and angle $\theta$. By comparing the arc length of this sector with the circumference of the base of the cone, show that $l\theta = 2\pi r$, and deduce by calculating the area of the sector, that the curved surface area of the cone is $\pi rl$.

 

[Euge]

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