Question

Question 108

Priyanka took a wire and bent it to form a circle of radius 14 cm. 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
$\therefore$ Length of the wire = Circumference of the circle = $2\pi r=2\times \frac{22}{7}\times 14=88cm$
Let b be the width of rectangle.
Since, the wire is rebent in the form of rectangle.
$\therefore$ Perimeter of rectangle = Circumference of the cirle
$\Rightarrow 2(24+b)=88$
$\Rightarrow 24+b=44\Rightarrow b=44-24$
$\Rightarrow b=20cm$
Area of circle $=\pi r^2=\frac{22}{7}\times (14{)}^2=616c{m}^2$

$\because$ Area of rectangle $=l\times b=24\times 20=480c{m}^2$
Hence, the circle encloses more area than rectangle.