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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°. - Mathematics

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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`)

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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

Concept: Circumference of a Circle
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