# 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(r₁ + r₂)l

where r₁, r₂ 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, 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.

**☛ Check: **Class 10 Maths NCERT Solutions Chapter 13

**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

**Summary:**

A fez, the cap used by the Turks, is shaped like the frustum of a cone shown in the figure. 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, the area of material used for making it is 710.29 cm².

**☛ Related Questions:**

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- The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
- A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of ₹ 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 8 per 100 cm².
- A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16 cm, find the length of the wire.

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