# Q. 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 $\pi =\frac{22}{7}$ )

G Gautam harsolia

It is given that the length of wire is 44 cm

Now, we know that

Circumference of the circle (C) = $2 \pi r$

$\Rightarrow 44 = 2 \pi r$

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

Now,

Area of circle (A) = $\pi r^2$

$\Rightarrow \pi r^2= \frac{22}{7}\times (7)^2= 154 \ cm^2$                                      - (i)

Now,

Perimeter of square(P) = $4a$

$\Rightarrow 44=4a$

$\Rightarrow a = \frac{44}{4} = 11 \ cm$

Area of sqaure = $a^2$

$\Rightarrow a^2 = (11)^2= 121 \ cm^2$                                                   -(ii)

From equation (i) and (ii) we can clearly see that area of the circular-shaped wire is more than square-shaped wire

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