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 $10cm$, radius at the upper base is $4cm$ and its slant height is $15cm$, find the area of material used for making it.

Answer 1

Given:
Radius (r) of upper circular end $=4$ cm
Radius (R) of lower circular end $=10$ cm
Slant height (l) of frustum $=15$ cm

Area of material used for making the fez = CSA of frustum + Area of upper circular end
$=\pi (R+r)l+\pi r^2$
$=\pi (10+4)\times 15+\pi \times 4^2$
$=210\pi +16\pi =\frac{226\times 22}{7}$
$=710\frac{2}{7}c{m}^2$
Therefore, the area of material used for making it is $710\frac{2}{7}c{m}^2$.