Surface Area of a Cone (2 of 2: Deriving the formula)

[Lee_yourboylee]

Wonderful explanation, Mr Woo, especially in combination with providing the students with their own net from which to construct their own cone. Splendid video.

[Aarush-INDIANEXO-L]

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.

[dawsontate]

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.

[pianoboss]

My brain was blown. This was an amazing explanation!

[mercie]

So wonderful, , you have an amazing content

[tanelkagan]

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!

[gadoliumnitrogen]

Had to watch this as well in class! Hi, 9.B math :)

[aguyontheinternet]

Managed to explain it without going into calculus, series, and infinity. Cool.

[thomasrowley]

Thank you for your clear explanation. I now understand why the area of a cone is πr^2+πrl . :)

[logiprime]

You have my subscription thank you so much for the help!

[zubair]

How is the length of arc equal to circumference of the top circle...