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Question
In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and
3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region. [User`22/7`]
Solution
PQ and AB are the arcs of two concentric circles of radii 7 cm and 3.5 cm respectively.
Let r1and r2 be the radii of the outer and the inner circle respectively.
Suppose θ be the angle subtended by the arcs at the centre O.
Then r1 = 7 cm, r2 = 3.5 cm and θ = 30°
Area of the shaded region
= Area of sector OPQ − Area of sector OAB
`=O//360^@pir_1^2-O//360^@pir_2^2`
`=O//360^@pi(r_1^2-r_2^2)`
`=30^@/360^@xx22/7p[(7cm)^2-(3.5)^2]`
`=1/12xx22/7xx(49-12.25)cm^2`
`=9.625 cm^2`
Thus, the area of the shaded region is 9.625 cm2.
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