3. A fez, the cap used by the Turks, is shaped like the
frustum of a cone (see Fig. 1324) If its radius on the
open side is 10 cm, radius at the upper base is
and its slant height is 15 cm, find the area of material
used for making it
Answers
Given:
Radius (r) of upper circular end of the frustum of a cone = 4 cm
Radius (R) of lower circular end of the frustum of a cone = 10 cm
Slant height (l) of frustum= 15 cm
To find : Area of material used for making it
Solution:
Area of material used for making the fez, A = CSA of frustum + Area of upper circular end
A = π(R + r)l + πr²
A = π(10 + 4) × 15 + π x 4²
A = π × 14 × 15 + π x 16
A = 210π + 16π
A = π(210 + 16)
A = 226 x 22/7
A = 4972/7
A = 710.28 cm²
Hence, the area of material used for making it is 710.28 cm².
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Given : A fez, the cap used by the Turks, is shaped like the frustum of a cone its radius on the open side is 10 cm, radius at the upper base is 4 cm
and its slant height is 15 cm,
To find : the area of material used for making cap
Solution:
area of material used = CSA + upper base area
CSA = π(r₁ + r₂)L
r₁ = 10 cm
r₂ = 4 cm
L = 15 cm
upper base area = π r₂²
area of material used = π(r₁ + r₂)L + π r₂²
= π (10 + 4) 15 + π (4)²
= π ( 210 + 16)
= π (226)
= (22/7)226
= 4,972 /7
= 710 2/7
= 710.286 cm²
area of material used for making CAP = 710.286 cm²
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