A circle with centre $O$ and radius $7 c m$ is circumscribing a square $A B C D$ of side $8 c m$ .

Find the area of the shaded region. [Take $π = \frac{22}{7}$ ]

$64 c m^{2}$

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$154 c m^{2}$

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$90 c m^{2}$

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$100 c m^{2}$

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Solution

The correct option is C
$90 c m^{2}$

Given: Radius of the circle, $r = 7 c m$

Side of the square, $s = 8 c m$

Area of the shaded region $=$ area of the circle $-$ area of the square

$= π r^{2} - s^{2}$

$= π \times 7 \times 7 - 8 \times 8$

$= \frac{22}{7} \times 7 \times 7 - 64$

$= 154 - 64 = 90 c m^{2}$

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