13. The radiis of two concentric circles are 7 cm and 10.5 cm, shown in the adjoining figure. Find the
area of the shaded region.
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Answer:
Given−
Twosectorshavesamevertexandthecentralangle=θ=30
o
.
Theradiusoftheoutersector=r
1
=7cmand
Theradiusoftheinnersector=r
2
=3.5cm.
Tofindout−
Thear.shadedregion=?
Solution−
Weknowthat
ar.sector=
360
o
θ
πr
2
whenθ=centralangle
andr=radiusofthecircle.
ar.outersector=
360
o
θ
πr
1
2
&
ar.innersector=
360
o
θ
πr
2
2
.
NowThear.shadedregion=thedifferencebetween
theareasofthetwogivensectors
=
360
o
θ
πr
1
2
−
360
o
θ
πr
2
2
=
360
o
θ
π(r
1
2
−r
2
2
)
=
360
o
30
o
×
7
22
×(7
2
−3.5
2
)cm
2
=9.625cm
2
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