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State true or false.

In the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a circle with centre C, then the area of the shaded region will be equal to $10 cm 2$ .

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True

False

answer is B.

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Detailed Solution

We have to check if the area of the shaded region will be equal to 10 cm2.
We know that,
Area of shaded region = [Area of square OABC] − [Area of quadrant COPB having radius OC]
Area of square= (side)2
Area of quadrant=

14 π r 2

Area of shaded region = (7) 2 − 14 227 × 72 = 49 − 38.5 = 10.5 cm 2

So, the area of the shaded region is

10.5 cm 2

and thus the statement is false.
Therefore, option 2 is correct.

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