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Question
In Fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (use `pi = 22/7`)
Solution
Area of the region ABDC = Area of sector AOC – Area of sector BOD
`=40^@/360^@xx22/7xx14xx14-40^@/360^@xx22/7xx7xx7`
`=1/9xx22xx14xx2-1/9xx22xx7xx1`
`=22/9xx(28-7)`
`=22/9xx21`
=`154/3`
=51.33 cm2
Area of circular ring = `22/7xx14xx14-22/7xx7xx7`
= 22x14x2-22x7x1
=22x(28-7)
=22x21
=462 cm2
∴ Required shaded region Area of circular ring Area of region ABDC
= 462 - 51.33
= 410.67 cm2
Thus, the area of shaded region is 410.67 cm2
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