Question

A wire is in the shape of a circle of radius 7m. If the same wire is rebent in the shape of a square, what
will be the measure of each side? Also find the area of the square. (Take π = 22/7)

Answer 1

Answer:

concept used

Here the concept of Perimetre and area is used. The radius of the circle is given as 7 metre. We will find the circumference of the circle.

circumference of the circle= perimetre of the square.

After equating the perimeters of circle and square we will get the measure of each side of square.

then, will find the area of the square

Formula used

$\bold{Circumference \: of \: circle= 2πr }$

$\bold{Perimeter \: of \: square= 4×side}$

$\bold{Area \: of \: square= side²}$

Solution

Radius = 7 m

$\sf{ \to \color{grey}circumference of circle = 2πr}$

$\sf{ \implies circumference \: of \: circle= 2 ×\frac{22}{7} ×7}\\ \\ \sf{ \implies \color{red}circumference\:of \:circle= 44 m}$

$\sf{ \to perimeter \: of \: square= perimetre \: of \: circle}$

$\sf{ \to perimeter \: of \: square= 44 m}$

we know that

$\sf{ \to \: perimeter \: of \: square \: is \: given \: as = 4×side}$

$\sf{\implies 44=4×side}\\ \\ \sf{\implies side=\frac{44}{4}}\\ \\ \sf {\implies\color{skyblue}side=11 m}$

Therefore the side of square is 11 m.

$\sf{\to area\:of\:square= side²}\\ \\\sf{\implies area\:of\:square= 11²}\\ \\\sf{\implies\color{red}Area\:of\:square= 121 m².}$

Therefore the area of square is 121 m²

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