Surface Area of a Cone - Visual Explanation and Example (Mastering Geometry)

Surface Area of a Cone - Visual Explanation and Example is a lesson that will help you make sense of the formula that we use to find the surface area of a cone. Once we make sense of the formula, we will do an example where we find the surface area of a cone.
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⏰Timestamps⏰
0:00 Introduction
0:02 Surface Area of a Cone (Visual Explanation)
3:25 Surface Area of a Cone (Example)
#geometry #area #maths

[@rightgirlwrongplanet]

I loved the moving part of this video to visualise the formulation of the area of the curved surface of the cone.
However I have a question:
At 1:53, the circumference is described as "2 x pi x r". This circumference is made of the dotted region (absent from the final 3D cone) and line region (present in the final 3D cone). Makes sense so far.
However, when that line is flattened out to make a straight line at 2:00, that line represents the arc length not the whole of the circumference, yet it is still referred to in length as "2 pi x r".
Should that straight line not be a fraction of the whole circumference?

[@gschett1]

Good insights. However, there are two different circles that we're talking about. The base circle has radius r.
The region (a sector) shown at 1:53 is not the base circle. It's the upper portion of the cone flattened out. It is bigger than the base circle. Its radius is l, the slant length. The arc length of the sector is the circumference of the base circle, which is why we're still calling it 2πr (again, r is the radius of the base circle, this thing has a different radius).

[@user-rz6lu9dp2m]

at 6:08 isn't the formula for circumference 2πr and if so should the equation be 1/2(2*3*π)*7.61 ?