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In the adjoining figure, two concentric ...

In the adjoining figure, two concentric circle with centre O have radii 21 cm and 42 cm. If `angleAOB = 60^(@)`, find the area of the shaded region. (Use `pi = (22)/(7)`)

Text Solution

Verified by Experts

Required area = area of large circle with radius 42 cm `-` area of smaller circle with radius 21 cm `-` (area of unshaded portion CDBA)
`= pi (42)^(2) - pi (21)^(2) -` [(area of larger sector with radius 42 cm) `-` (area of smaller sector with radius 21 cm)]
`= pi (42)^(2) - pi(21)^(2) - [pi (42)^(2) xx (60)/(360) - pi (21)^(2) xx (60)/(360)]`
`= pi (42)^(2) - pi (21)^(2) - (1)/(6) pi (42)^(2) + (1)/(6) pi (21)^(2) = (5)/(6) pi (42)^(2) - (5)/(6) pi (21)^(2)`
`= (5)/(6) pi xx (21)^(2) [4 - 1] = (5)/(6) xx (22)/(7) xx 21 xx 21 xx 3 = 3465 cm^(2)`
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