Question

Shazli took a wire of length $44cm$ and bent it into the shape of a circle. Find the radius of that circle. Also finds 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, and the square? (Take $\pi =\frac{22}{7}$)

Answer 1

.When the wire is bent into a circle.

The length of the wire $=$ circumference of the circle

$44cm=2\pi r$ [$\because$ circumference of the circle $=2\pi r$]

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

Radius of circle $=7cm$

Area of circle $=\pi r^2=\frac{22}{7}\times 7^2=22\times 7=154{cm}^2$

When the wire is rebent into a square.

The length of the wire $=$ Perimeter of the square

$44=4\times side$ [$\because$ Perimeter of the square $=4\times side$]

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

Length of each side of square $=11cm$

$\therefore$ Area of the square $={side}^2={11}^2=121{cm}^2$

Difference in area enclosed (circle and square) $=154-121=33{cm}^2$

$\therefore$ Circle enclosed more area than square.