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What will be the area of the shaded region, if in the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7cm and 3.5 cm with centre O, with $∠ P O Q = 30 °$ ?

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770 cm 2

778 cm 2

774 cm 2

775 cm 2

answer is B.

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Detailed Solution

We have to find the area of the shaded region, if in the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7cm and 3.5 cm with centre O, with

∠ P O Q = 30 °

Calculating the area of the shaded region,
Area of the shaded portion = Area of sector OPQ − Area of sector OAB
Area of the sector

= π r 2 θ 360 °

where r is the radius and

θ

is the angle subtended by the arc.

= 30 ° 360 ° × π (7) 2 − 30 ° 360 ° × π (3.5) 2 = 227 × 112 (7) 2 − (3.5) 2

Solving,

= 227 × 112 (7) 2 − (72) 2 = 227 × 112 × 1474 = 778 cm 2

So, the area of the shaded portion is 778 cm2.
Therefore, option 2 is correct.

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