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?

Answer 1

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.