a piece of wire of 20 cm is bent to form the shape of a sector. if the arc has length f 8 cm, calculate the angle of sector and the area enclosed by this sector.
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Answer:
Step-by-step explanation:
Given−
AB is a wire of length=l=20cm.
It is bent in arc which subtends an angle=θ=60
o
at the centre of the circle which the arc AB belongs to.
To find out−
the radius of the circle.
Solution−
The length of the arc=l=20cm.
It forms the part of a circle with radius=r.
Also it subtends anangleθ=60
o
.
Now,forθ=60
o
,the arc length is =20cm.
∴forθ=360
o
,the arc length isC=
θ
l
×360
o
cm
=circumference=Cofthecircle.
SoC=
60
o
20
×360
o
cm=120cm.
ButC=2πr.
∴2πr=120⟹r=
π
60
cm.
Ans−OptionA.
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