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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?
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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 xx (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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