Question:
A fez, the cap used by the Turks, is shaped like the frustum of a cone (see fig.). 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:
$\mathrm{R}=10 \mathrm{~cm}, \mathrm{r}=4 \mathrm{~cm}, \ell=15 \mathrm{~cm}$
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
$=600+50 \frac{2}{7} \mathrm{~cm}^{2}=710 \frac{2}{7} \mathrm{~cm}^{2}$