sector ratio's, some basic calc and geometry,?

Question

could someone show me how to solve these 4 problems
i'm lost to the whole ratio of formulas
so far i've found that the area of a cone is A=(PI*r^2)+(PI*r*s)
i think i should divide that by 2 but i dont think its as easy as that.

here's a scan to show all of what you need to know
http://i8.photobucket.com/albums/a33/ChaoticPYRO/scancalc.jpg

ok i see what you mean now. for some reason i was seeing the image as 3D and not a 2D part of a circle.

so how can i find equations for said sector?

Answer 1

Jordan, I think you are lost in space. You have a circle with 2 radii of unit length. If they are OA and OB, they create an angle theta or AOB. There is a triangle AOB whose area can be computed, and a sector AOB whose area can be computed
(theta/360) * pi* 1*2. As theta decreases, the ratio of sector area to triangle area approaches 1. This is reasonable, since the length of the triangle AB approaches the sector length AB.