Question

Priyanka took a wire and bent it to form a circle of radius $14cm$. Then she bent it into a rectangle with one side $24cm$ long. What is the length of the wire? Which shape encloses more area, the circle or the rectangle?

Answer 1

Given, Radius of circle $=14cm$ and Length of rectangle $l=24cm$

Hence,$\text{length of the wire= circumference of circle}$

$=2\pi r=2\times \frac{22}{7}\times 14=88cm$

So, length of wire is $88cm$

Let $b$ the width of rectangle.

Since, the wire is bent again in the form of rectangle

Hence, $\text{perimeter of rectangle = circumference of circle=length of wire}$

$\Rightarrow 2(l+b)=88$

$\Rightarrow 2(24+b)=88$

$\Rightarrow 24+b=44$

$\Rightarrow b=44-24$

$\Rightarrow b=20cm$

Now, Area of circle $\pi r^2=\frac{22}{7}\times 14\times 14=616c{m}^2$

And, area of rectangle $lb=24\times 20=480c{m}^2$

Therefore, the circle encloses more area than rectangle.