Question

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In fig. two concentric circles with centre O ,have radii 21cm and 42 cm . If ∠AOB=60° find The area of shaded region .


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Answer 1

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In fig. two concentric circles with centre O ,have radii 21cm and 42 cm . If ∠AOB=60° find The area of shaded region .

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refer the attachment

Answer 2

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• Find the area of shaded region.

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Here,

Area of ring

$\sf = \pi( {42}^{2} - {21}^{2} )cm^{2}$

$\sf = 4158 {cm}^{2}$

Now,

Area of shaded region = (Sector formed by bigger circle) -(sector formed by smaller circle)

$\sf = \frac{\pi \times \: {(42)}^{2} \times 60 \degree}{360 \degree} - \frac{\pi \times {(21)}^{2} \times 60 \degree}{360 \degree}$

$\sf = \frac{\pi}{6} \times ( {42}^{2} - {21}^{2} )$

$\sf = 693cm^{2}$

Hence,

Required area

$\sf = (4158 - 693) {cm}^{2}$

$\sf = 3465cm^{2}$

$\star\:\:\:\sf\large\underline\blue{Answer:-}$

• Area of shaded region $\sf = 3465cm^{2}$