Question

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.

Answer 1

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