Question

Proof that the surface area of a cone is equal to pir^2+2pirS

Answer 1

I don't think that's true. I think it is \[A(r,s)=\pi r^2+\pi rs\]Think of the side of the cone as a triangle with its base the length of the circumference of the base. So the area of the cone is\[A _{cone}=A _{base}+A _{side}=\pi r^2+\pi rs\]

Answer 2

Can you show some diagrams? I don't understand

Answer 3

also, it is 2pirS

Answer 4

What do you mean by thinking the side as a triangle?

Answer 5

Not around here. If the sides went straight up for distance s, the area of the side would be 2 pi rs. Unfortunately, that is a cylinder, and not a cone. The distance around the cone is 2 pi r at the base, and zero at the vertex. Since the surface is straight from the base to the vertex, we can average the distance around to pi r. Multiply by the slant height to get the area.

Answer 6

If you don't believe me, check it out here: http://math.about.com/od/formulas/ss/surfaceareavol_2.htm

Answer 7

ok, i see.

Answer 8

If you cut the cone apart, and flatten out the side of it onto the table, it will make a triangle (at least approximately).

Answer 9

Something like this?

Answer 10

Yessir.

Answer 11

oh, i understand now. Thank you very much for pointing it out!