Question

Shazli took a wire of length $$44$$cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take $$\pi =\dfrac{22}{7}$$)

Answer 1

Given, Total length of the wire$$=44$$cm

$$\therefore$$ The circumference of the circle$$=2\pi r=44$$cm

$$\Rightarrow 2\times \dfrac{22}{7}\times r=44$$

$$\Rightarrow r=\dfrac{44\times 7}{2\times 22}=7$$cm

Now, Area of the circle$$=\pi r^2=\dfrac{22}{7}\times 7\times 7=154 cm^2$$

Now the wire is converted into square,
Then perimeter of square$$=44$$cm
$$\Rightarrow 4\times$$ side$$=44$$
$$\Rightarrow$$ side$$=\dfrac{44}{4}=11$$cm

Now, area of square$$=$$side$$\times$$side$$=11\times 11=121cm^2$$

Therefore, on comparing the area of circle is greater than that of square, so the circle enclosed more area.