(Solution Download) If the surface of a cone of slant height C


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 ? (see Figure 19).
(a) Show that ? = 2?r/l radians.
(b) Use the formula 1/2l20 for the area of a sector of radius C and central angle ? to show that the lateral surface area of a cone is ?rl.
(c) Use the result of part (b) to obtain the formula A = 2?(r1 + r2)/2]l for the lateral area of a frustum of a cone with base radii r1 and r2 and slant height l.

 







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