Question

Question 9

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

Total length of the wire = 44 cm
$\therefore$ Circumference of the circle = $2\pi r=44cm$
$\Rightarrow$ $2\times \frac{22}{7}\times r=44$
$\Rightarrow$ $r=\frac{44\times 7}{2\times 22}=7cm$
Now, area of the circle = $\pi r^2$
$=\frac{22}{7}\times 7\times 7=154c{m}^2$
Now the same wire is bent into a square.
Then perimeter of square = 44 cm
$\Rightarrow$ $4\times side=44$
$\Rightarrow$ $side=\frac{44}{4}=11cm$
Now, area of square = $side\times side=11\times 11=121c{m}^2$
Therefore, on comparing, the area of circle is greater that of square so the circle encloses more area.