the radius of the given figure is 35 metre the radius of smaller circle is 14 metre find the area of the shaded portion
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In the figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC=40
∘
. Consider π=
7
22
.
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Solution
verified
Verified by Toppr
Given: Radius of inner circle =7 cm
Radius of outer circle =14 cm
Angle made by sector = 40
o
Area of sector OAC =
360
o
40
o
×πr
2
=
9
1
××
7
22
×14
2
=68.44
Area of sector OBD =
360
o
40
o
×πr
2
=
9
1
××
7
22
×7
2
=17.11
Area of the small region ABDC
= Area of the small sector OAC – Area of the small sector OBD =(68.44−17.11)cm
2
Area of shaded region ABDC= Area of outer circle − Area of inner circle − area of small region ABCD
Area of shaded region ABDC=π×14
2
−π×7
2
−(68.44−17.11)cm
2
Area of shaded region ABDC=410.484