A piece of wire is in the form of an arc of a
circle of radius 20 cm, subtending an angle of
150° at the centre of the circle. If it is bent into the form of a largest circle, found is radius.
Answers
Step-by-step explanation:
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MATHS
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60
0
at its centre. The radius of the circle is
ANSWER
Given−
ABisawireoflength=l=20cm.
Itisbentinanarcwhichsubtendsanangle=θ=60
o
atthecentreofthecirclewhichthearcABbelongsto.
Tofindout−
theradiusofthecircle.
Solution−
Thelengthofthearc=l=20cm.
Itformsthepartofacirclewithradius=r.
Alsoitsubtendsanangleθ=60
o
.
Now,forθ=60
o
,thearclengthisl=20cm.
∴forθ=360
o
,thearclengthisC=
θ
l
×360
o
cm
=circumference=Cofthecircle.
SoC=
60
o
20
×360
o
cm=120cm.
ButC=2πr.
∴2πr=120⟹r=
π
60
cm.
Answer:
8.33 cm
Step-by-step explanation:
first find the length of the arc
length of arc =(?/360?)×3?r
=15/360×2?20
=52.38
this will be equal to the circumference of the largest circle
so 52.38= 2?R
R = 52.38/2?
R=8.33 cm