A fez, the cap used by the Turks, is shaped like the frustum of a cone (see figure). 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.

Here R = 10 cm, r = 4 cm and l = 15 cm



Area of the material used for making the fez = Surface area of frustum + The surface of top circular section

\( = \ \pi (R \ + \ r)l \ + \ \pi r^2 \)

\(= \ \frac{22}{7} (10 \ + \ 4) 15 \ + \ \frac{22}{7} \ × \ 4 \ × \ 4 \)

\(= \ \frac{22}{7} \ × \ 14 \ × \ 15 \ + \ \frac{352}{7} \)

\(= \ \frac{4620 \ + \ 352}{7} \ = \frac{4972}{7} \) cm²