Mensuration-30

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A rectangle with length and breadth 12 cm and 5 cm is drawn within a circle. Find the area of the remaining space outside the rectangle

Solution: Length of the rectangle = 12 cm

Width of the rectangle = 5 cm

The diagonal of the rectangle passes through the center of the circle.

The diagonal = √(Length2 + Breadth2) = √(122 + 52)

= √(144 + 25) = √169 = 13 cm

Therefore, Diameter of the circle = 13 cm

=> Radius of the circle = 13 / 2 cm = 6.5 cm

Area of the circle = Π r2 = 3.14 x (6.5)2 cm2 = 132.665 cm2

Area of the remaining space outside the rectangle = Area of the circle - Area of the rectangle

= (132.665 - 60) cm2 = 72.665 cm2 = 72.67 cm2 (correct to two decimal places)

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