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ABCD is the diameter of a circle of radius 60 cm which is inscribed in square MNOP. The lengths of AB, BC and CD are equal. Semi-circles are drawn with AB and BD as diameters. Find the ratio of area of the unshaded region to that of shaded region.

ABCD is the diameter of a circle of radius 60 cm which is inscribed in square MNOP. The lengths of AB, BC and CD are equal. Semi-circles are drawn with AB and BD as diameters. Find the ratio of area of the unshaded region to that of shaded region. Correct Answer 3.58 

AB = BC = CD = 120/3 = 40 cm

Area of the shaded region = area of semi-circle with diameter AD – area of semi-circle with diameter BD

 ⇒ π602/2 – π402/2

⇒ π(3600 – 1600) /2

⇒ 2000π/2 = 3140 cm2

Unshaded area region = Area of the square − Area of the shaded region

⇒ 1202 − 3140 = 11260

∴ Required ratio = 11260 ∶ 3140 = 3.58

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