Find the surface area of the fabric required to make a lamp shade in the shape of a frustrum whose top and bottom diameter are 20cm and 30cm respectively and a height of 12cm.Give your answer to 2 decimals.

Answer 1

Consider a complete cone of height 36. The lamp shade is the bottom 1/3 of that cone. (draw a side view and use similar triangles)
cone has area A = 2πrs = 2π*15*39
The lampshade has area a = A - 2π*10*26

or you can figure a general formula using h,R,r as given in the problem.