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.

Answer 1

Radius on the open side of the cap, R = 10 cm.
Radius of upper end, r = 4 cm.
Slant height I = 15 cm
R = 10 cm, r = 4 cm, I = 15 cm
$$\therefore$$ Curved surface $$= \pi$$ x l x (R + r)
$$= \pi$$ x 15 x (10 + 4)
$$= \frac{22}{7}$$ x 15 x 14
$$= 660 cm^2$$
$$\therefore$$ Area of cap at the end
$$= \pi r^2$$
$$= \frac{22}{7} \times (4)^2$$
$$= \frac{22}{7} \times 16$$
$$= \frac{352}{7}$$
$$= 50 \frac{2}{7} cm^2$$
$$\therefore$$ Area of material used for making it,
$$= 600 + 50 \frac{2}{7}$$
$$= 710 \frac{2}{7} cm^2$$