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. $[Use\pi =22/7.]$

Answer 1

Radius $\left(r_2\right)$ at upper circular end = 4 cm

Radius $\left(r_1\right)$ at 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

$=\pi (r_1+r_2)l+\pi r_2^2=\pi (10+4)\times 15+\pi (4{)}^2=\pi (14)\times 15+16\pi =210\pi +16\pi =226\pi =226\times \frac{22}{7}=710\frac{2}{7}c{m}^2$

Therefore, the area of material used for making it is​​​​​​​ $710\frac{2}{7}c{m}^2$​​​​​​​.