If the surface of a cone of slant height C and base radius r is cut along a lateral edge and laid flat, it becomes the sector of a circle of radius C and central angle θ (see Figure 19).
(a) Show that θ = 2πr/l radians.
(b) Use the formula 1/2l20 for the area of a sector of radius C and central angle θ to show that the lateral surface area of a cone is πrl.
(c) Use the result of part (b) to obtain the formula A = 2Ï€(r1 + r2)/2]l for the lateral area of a frustum of a cone with base radii r1 and r2 and slant height l.