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

$\mathrm{R}=10 \mathrm{~cm}, \mathrm{r}=4 \mathrm{~cm}, \ell=15 \mathrm{~cm}$

Curved surface area $=\pi \times \ell \times\{R+r\}$

$=\pi \times 15 \times\{10+4\} \mathrm{cm}^{2}$

$=\frac{22}{7} \times 15 \times 14 \mathrm{~cm}^{2}=660 \mathrm{~cm}^{2}$

Area of the closed side

$=\pi r^{2}=\frac{22}{7} \times(4)^{2}$

$=\frac{\mathbf{3 5 2}}{\mathbf{7}}=50 \frac{\mathbf{2}}{\mathbf{7}} \mathrm{cm}^{2}$

total area of the material used

$=600+50 \frac{2}{7} \mathrm{~cm}^{2}=710 \frac{2}{7} \mathrm{~cm}^{2}$