a square OPQR is inscribed in a quadrant OAQBof a circle. if the radius of circle is 6√2 cm find the area of the shaded region
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Answer:20.57
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The area of the shaded region is 20.57 cm
Area of shaded portion = Area of quadrant OABQ - Area of square OPQR
= πr^2/4 - 1/2d^2
where,
r = radius of the circle = 6√2 cm
d = diagonal of the square = r = 6√2 cm
Area of shaded portion = πr^2/4 - 1/2d^2
= πr^2/4 - 1/2r^2
= r^2 ( π/4 - 1/2 )
= (6√2)^2 ( 22/7 × 1/4 - 1/2)
= 72 ( 11/7 × 1/2 - 1/2)
= 72 ( 2/7)
= 144/7
= 20.57 cm
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