Radii of two concentric circle is 7 cm and 14 cm the shaded area between them is equal to

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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 π=22/7

Solution

Given, $r=7cm$ and $R=14cm$. Area of shaded region

= $\frac{22}{7}({14}^2-7^2)\times \frac{({360}^{\circ }-{40}^{\circ })}{{360}^{\circ }}$

= $\frac{22}{7}\times 7\times 21\times \frac{{320}^{\circ }}{{360}^{\circ }}$

= $410.67c{m}^2$

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`)

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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