Find the lateral area of a cone. Why is it
Pi * r * l
The book I am reading says it is 1/2 the circumference of the base times the slant height. I cannot picture how or why this would get you the lateral area. Can someone help me visualize and understand this?
Looking at the net of the lateral area it looks like 1/3 of a whole circle where the slant height represents that circles radius. So (1/3)(pi * l ^2) would make sense to me.
I appreciate the response but I am not fully understanding it.
I recall an explanation a long time ago that made sense to me that used ratios. I believe it had something to do with the ratio of r:l I am not quite sure.
I think part of my issue is I am looking to understand why pi r l works for area of the lateral surface and not having any experience with A of a circle sector, now my mind is wondering where that formula came from if you follow me.
I understand that the area of a circle sector
is taking the area of the whole circle and by multiplying it by and gets you the portion of the circle you have. But I am not sure where comes from now.
I assume that represents the fraction portion of the circle. How do we know that represents 2pi(r) over L aka the circumference of the circle sector divided by it's radius.
EDIT:
Just remembered a piece of the ratio thing I was talking about earlier. I was told something about the proportion of the missing area is equal to the proportion of the missing circumference. Ill see if i can remember in full what I was supposed to do.
Just remembered what I heard before, tell me if this makes sense. Seems to make sense to me.
Since the proportion of the original circle's area that is left in the circle sector equal to the proportion of the circle sector's circumference (for example, if i have half the area, i have half the circumference as well)
I can do the following:
=
Sorry if you viewed that mid edit, i was playing with what I assume is the LATEX stuff i heard about. When I quoted your post it gave me the code you used. Much more convenient