# 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

**Solution:**

Since the fez is in the shape of the frustum of a cone and is open at the bottom.

Therefore,

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 frustum of a cone = π(r_{1} + r_{2})l

where r_{1}, r_{2} and l are the radii and slant height of the frustum of the cone respectively.

Area of the circle = πr²

where r is the radius of the circle

Slant height, l = 15 cm

Radius of open side, r_{1} = 10 cm

Radius of upper base, r_{2} = 4 cm

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

= π(r_{1} + r_{2})l + πr²

= π(r_{1} + r_{2})l + r_{2}²

= 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(2/7) cm²

710(2/7) cm² of the material used for making Fez.

**Video Solution:**

## 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

### NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.4 Question 3 - Chapter 13 Exercise 13.4 Question 3 :

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

The area of the material used for making Fez having radius on the open side as 10 cm, radius at the upper base as 4cm and slant height 15 cm is 710 2/7 cm².