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Question:

A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm, and its slant height is 15 cm, find the area of material used for making it.

Solution:

Given:Radius (r) of upper circular end = 4 cmRadius (R) of lower circular end = 10 cmSlant height (l) of frustum = 15 cmArea of material used for making the fez = CSA of frustum + Area of upper circular end = π(R+r)l + πr² = π(10+4) × 15 + π × 4² = 210π + 16π = 226π ≈ 226 × 22/7 = 710.27 cm²Therefore, the area of material used for making it is approximately 710.27 cm².