I could not for the life of me visualize how to find the lateral surface area of a cone for my calculus homework. This visual explanation was very simple and it made sense 👍
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?
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).
I could not for the life of me visualize how to find the lateral surface area of a cone for my calculus homework. This visual explanation was very simple and it made sense 👍
@@sukrithkishor7021 I am glad this was helpful to you.
Also, here is the link to the animation I used in the video
www.geogebra.org/m/zNumXZ4f
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?
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).
Thanks helped me
@Saka7-n2t not a problem.
I am glad this was helpful to you
at 6:08 isn't the formula for circumference 2πr and if so should the equation be 1/2(2*3*π)*7.61 ?
Is this in
gcse papers
@Saka7-n2t sometimes volume appears