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? $(Take\ \pi=\frac{22}{7})$

AcademicMathematicsNCERTClass 7

Length of the wire to be bent into circle $=44\ cm$

$2\pi r=44$

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

$r=\frac{44\times7}{2\times22}=7cm$

Area of such circle$=\pi r^2$ 

$=\frac{22}{7}\times7\times7$

$=154\ cm^2$

Now , the length of the wire is bent into a square.

Here perimeter of square$=$ Circumference of line k

Length of each side of the square$= \frac{Perimeter}{4}$

$=\frac{44}{4}$

$=11\ cm$ 

Area of the square$=(side)^2$

$=(11)^2$

$=121\ cm^2$

Since, $154\ cm^2$>$121\ cm^2$

Thus, the circle encloses more area.
raja
Updated on 10-Oct-2022 13:36:02

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