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AB and CD are arcs of two concentric circles of radii 21 cm and 7 cm respectively and centre O. If ∠AOB =30°, find the area of the shaded region.

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3083 c m 2

3053 c m 2

3103 c m 2

3043 c m 2

answer is A.

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Detailed Solution

Given that two concentric circles of radii 21 cm and 7 cm centre at o with ∠AOB = 30°.

From figure,
Area of shaded region = Area of sector AOB – Area of sector COD.
Area of sector =

θ 360 × π r 2

For sector AOB, r = 21 cm and θ=30°.
⇒Area of sector AOB =

30360 × 227 × 21 × 21

⇒Area of sector AOB =

112 × 22 × 3 × 21

⇒Area of sector AOB =

2312 c m 2

Now, for sector COD, r = 7cm and θ=30°.
⇒Area of sector COD =

30360 × 227 × 7 × 7

⇒Area of sector COD =

112 × 22 × 7

⇒Area of sector COD =

776 c m 2

Thus, area of shaded region =

2312 c m 2 −

776 c m 2

⇒Area of shaded region =

3 × 231 − 77 6

⇒Area of shaded region =

6166

cm2
Hence, the area of the shaded region is

3083 c m 2

.
Therefore, the correct answer is option (1).

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