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 $\pi =\frac{22}{7}$)

Answer 1

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

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

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

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

Now, Area of the circle$=\pi r^2=\frac{22}{7}\times 7\times 7=154c{m}^2$

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

Now, area of square$=$side$\times$side$=11\times 11=121c{m}^2$

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