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Question
Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?
Solution
Given that, radius of circle (r) = 14 cm and length of rectangle (l) = 24 cm
∴ Length of the wire = Circumference of the circle = 2πr = `2 xx 22/7 xx 14` = 88 cm
Let b be the width of rectangle
Since, the wire is rebent in the form of rectangle
∴ Perimeter of rectangle = Circumference of circle
⇒ 2(24 + b) = 88
⇒ 24 + b = 44
⇒ b = 44 – 24
⇒ b = 20 cm
Area of circle = πr2 = `22/7` × (14)2 = 616 cm2
∵ Area of rectangle = l × b = 24 × 20 = 480 cm2
Hence, the circle encloses more area than rectangle.
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