A fez, the cap used by the Turks, is shaped like the frustum of a cone (see Fig. 13.24). 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.

Area of material used for making fez = Curved Surface Area of the frustum + Area of the upper circular end

Let us find the area of material by using formulae;

CSA of a frustum of a cone= π(r₁ + r₂)l

where r₁, r₂ and l are the radii and slant height of the frustum of the cone respectively.

Area of a circle= πr²

where r is the radius of a circle

Slant height, l = 15 cm

Radius of open side, r₁ = 10 cm

Radius of upper base, r₂ = 4 cm

Area of material used for making fez = Curved Surface area of the frustum + area of the upper circular end

= π(r₁ + r₂)l + πr₂²

= π[(r₁ + r₂)l + r₂²]

= 22/7 [(10 cm + 4 cm)15 cm + (4 cm)²]

= 22/7 [14 cm × 15 cm + 16 cm²]

= 22/7 [14 cm × 15 cm + 16 cm²]

= 22/7 [210 cm² + 16 cm²]

= 22/7 × 226 cm²

= 4972/7 cm²

= 710.29 cm²

710.29 cm² of the material used for making Fez.