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 $\pi =22/7$)

Answer 1

We have to determine after bending the wire which shape encloses more area

If the wire is bent into a circle,

Step 1. Finding Circumference & Area of the circle

We know that,

$$\begin{gathered} Circumferenceofthecircle=2\pi r \\ 44=2\times (22/7)\times r \\ 44=44/7\times r \\ (44\times 7)/44=r \\ r=7cm \end{gathered}$$

$$\begin{gathered} Areaofthecircle=\pi r^2 \\ =22/7\times 7^2 \\ =\frac{22}{7}\times 7\times 7 \\ =22\times 7 \\ =154c{m}^2 \end{gathered}$$

Now,

If the wire is bent into a square,

Step 2. The length & Area of the square

The length of each side of square $=\frac{44}{4}$

$=11cm$

$Areaofthesquare=lengthofthesideofsquare2$

$={\left(11\right)}^2=121c{m}^2$

Step 3. On comparing the two areas of the square and circle,

Area of circle$>$Area of square.

Hence, Circle encloses more area