Q108 of 131 Page 226

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?

Given, radius of the circle = 14 cm


and length of the rectangle = 24 cm


Since the same wire is rebent to form different shapes,


Perimeter of rectangle = Circumference of circle


2 × (l + b) = 2∏r


2 × (24 + b) = 2 × × 14


24 + b = 44


⇒ b = 44 - 24 = 20 cm


Area of rectangle = l × b = 24 × 20 = 480 cm2


And area of circle = ∏r2 = × 14 × 14 = 616 cm2


Hence, circle encloses more area than the rectangle.


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