The figure shows nine 1cm $\times$ 1 cm squares and a circe. The circle passes through the centres of the squares in the four corners.

What is the area (in sq. cm) of the shaded region?

81 - \sqrt{2} π

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\frac{9 - 2 π}{4}

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9 - 2 π

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\frac{81 - 2 π}{2}

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Solution

The correct option is B $\frac{9 - 2 π}{4}$
Area of square = 9sq cm
area of circle = $π r^{2}$ = $π \times {(\sqrt{2})}^{2} = 2 π s q c m$ (two diagonals of in smaller squares make the diameter on the circle)
area of the shaded region = $\frac{(9 - 2 π)}{4} c m$

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The figure shows nine 1cm × 1 cm squares and a circe. The circle passes through the centres of the squares in the four corners. What is the area (in sq. cm) of the shaded region?

The correct option is B 9−2π4Area of square = 9sq cm area of circle =πr2 =π×(√2)2=2πsq cm (two diagonals of in smaller squares make the diameter on the circle) area of the shaded region =(9−2π)4cm

The figure shows nine 1cm $\times$ 1 cm squares and a circe. The circle passes through the centres of the squares in the four corners.

What is the area (in sq. cm) of the shaded region?

The correct option is B $\frac{9 - 2 π}{4}$
Area of square = 9sq cm
area of circle = $π r^{2}$ = $π \times {(\sqrt{2})}^{2} = 2 π s q c m$ (two diagonals of in smaller squares make the diameter on the circle)
area of the shaded region = $\frac{(9 - 2 π)}{4} c m$