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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