A hand fan is made up of cloth fixed in between the metallic wires. It is in
the shape of a sector of a circle of radius 21 cm and of angle 120° as
shown in the figure. Calculate the area of the cloth used and also find the
total length of the metallic wire required to make such a fan.?
Answers
Answer:
462cm square
Step-by-step explanation:
r=21cm
teta120°
area of sector = teta/360°×πr2
=120°/360°×22/7×21×21
=462cm square
the area of cloth is used =462cm square
length of arc =teta/360°×2×π×r
=120°/360°×2×22/7×21
88/2cm square
Given : A hand fan is made up of cloth fixed in between the metallic wires. It is in the shape of a sector of a circle of radius 21 cm and of angle 120°
To find : the area of the cloth used
the total length of the metallic wire required to make such a fan
Solution:
Radius = 21 cm
Sector angle = 120°
Area of Sector = (Sector angle/360°) * π (Radius)²
using π = 22/7
= ( 120/360) * (22/7) * 21²
= 462 cm²
the area of the cloth used = 462 cm²
total length of the metallic wire required = Radius + arc length + Radius
arc length = ( arc angle / 360°) * 2 π Radius
=> arc length = ( 120/360) * 2 * (22/7) * 21 = 44 cm
total length of the metallic wire required = 21 + 44 + 21
= 86 cm
the area of the cloth used = 462 cm²
total length of the metallic wire required = 86 cm
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