Wonderful explanation, Mr Woo, especially in combination with providing the students with their own net from which to construct their own cone. Splendid video.
Am an Indian student in 10th grade and I have been lately realizing how obsolete Indian education system is. But I am so grateful that i finally understood the curved surface area's formula derivation from you. Keep inspiring and helping us sir. Much love from India.
Thank you so much for explaining why the formula is what it is. So many math videos focus on just showing the formula and telling you to plug in values, rather than explaining the why.
Great stuff as ever but I would have liked to have seen this go just a little further, which is to (also) express the surface area in terms of r and h, since these are going to be typically the most common values provided. By Pythagoras' Theorem, l² = h² + r² so we can rearrange to get l = √(h² + r²). Plugging that in to A = π r² + π r l gives: A = π r² + π r√(h² + r²) and factoring out the πr we get:- A = π r (r +√(h² + r²)) Yes, it's a little more complicated, but not by much. Another way of looking at it is that given h and r you would use Pythagoras to get l, so in essence you're performing the same calculations but just saving a step or two - perhaps!
@@michelleyang2707 😂 Misconception.. The thing is that we have to learn same thing but in a advance way. Maybe his student are dumb and now their eye's got open and started studying !
Wonderful explanation, Mr Woo, especially in combination with providing the students with their own net from which to construct their own cone. Splendid video.
Am an Indian student in 10th grade and I have been lately realizing how obsolete Indian education system is. But I am so grateful that i finally understood the curved surface area's formula derivation from you. Keep inspiring and helping us sir. Much love from India.
My brain was blown. This was an amazing explanation!
BRO YOU ARE ACTUALLY THE GOAT
Had to watch this as well in class! Hi, 9.B math :)
Thank you so much for explaining why the formula is what it is. So many math videos focus on just showing the formula and telling you to plug in values, rather than explaining the why.
great explanation - keep it up my man
You have my subscription thank you so much for the help!
Great stuff as ever but I would have liked to have seen this go just a little further, which is to (also) express the surface area in terms of r and h, since these are going to be typically the most common values provided.
By Pythagoras' Theorem, l² = h² + r² so we can rearrange to get l = √(h² + r²).
Plugging that in to A = π r² + π r l gives:
A = π r² + π r√(h² + r²)
and factoring out the πr we get:-
A = π r (r +√(h² + r²))
Yes, it's a little more complicated, but not by much. Another way of looking at it is that given h and r you would use Pythagoras to get l, so in essence you're performing the same calculations but just saving a step or two - perhaps!
So wonderful,, you have an amazing content
Managed to explain it without going into calculus, series, and infinity. Cool.
Thank you for your clear explanation. I now understand why the area of a cone is πr^2+πrl . :)
its not the area its the surface area 😊
How is the length of arc equal to circumference of the top circle...
Make a cone and unfold it and you'll see
The arc wraps around the base circle (base of the cone) perfectly. Hence the length of the arc is the circumference of the base circle
What grade is this?
11th? Idk lol. I'm in 8th-grade learning IM 3 which is 11th-grade math.
@@michelleyang2707 😂 Misconception..
The thing is that we have to learn same thing but in a advance way. Maybe his student are dumb and now their eye's got open and started studying !
year 10
ugh very confusing
same
Its ur fault cuz ur dumb