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प्रश्न
In the given figure, two concentric circles with centre O have radii 14 cm and 7 cm. If ∠AOB = 30°, find the area of the shaded region.
बेरीज
उत्तर
Area of Region ABCD = Area of the bigger sector − Area of smaller Sector
= `(30/360 xx 22/7 xx 14 xx 14 − 30/360 xx 22/7 xx 7 xx 7)`
= `(1/12 xx 22 xx 2 xx 14 − 1/12 xx 22 xx 7)`
= `1/12 xx 22 xx (28 − 7)`
= `1/12 xx 22 xx 21`
= `77/2` sq. cm
= 38.5 sq. cm
Area of circular ring = `(22/7 xx 14 xx 14 - 22/7 xx 7 xx 7)`
= 22 × 14 × 2 − 22 × 7 × 1
= 22 × 21
= 462 sq. cm
Hence, the Required shaded area = 462 − 38.5
= 423.5 sq. cm
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