Question

A steel wire when bent in the form of a square encloses the area of 121 cm square if a same wire bent into a form of a circle. find the areaof circle intext:zigya

Answer 1

Given, Wire is bent in the shape of a square with area 121 cm².

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Area of square = (a)² where a is the side of the square.

So, a² = 121

a = √121

a = 11

Now the perimeter of the square will be equal to the perimeter of the circle.

So perimeter of the square = 4a

= 4 x 11

= 44 cm

Perimeter of the circle = 2πr where r is the radius of the circle.

2.π.r = 44

2.22/7.r = 44

r = 44*7/44

r = 7 cm

Area of circle = πr²

= 22/7 · 7 · 7

= 22 x 7

= 154 cm²

Hence the area of circle is 154 cm².

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Answer 2

□□□□

$\large \boxed{ \textsf{given:-}}$

$\texttt {\: enclosed area of steel wire when bent to form square = 121 \: sq.cm }$

$\large \boxed{ \textsf{to find out:-}}$

$\textsf{the area of circle}=??$

$\large \boxed{ \rm \: solution:-}$

$\rm \: Side \: a \: square \: = \sqrt{121}cm = 11cm$

$\rm \: perimeter \: of \: square = (4 \times 11)cm = 44cm$

$\rm \therefore \: length \: of \: the \: wire \: = 44cm$

$\rm \therefore \: circumference \: of \: the \: circle \: = length \: of \: wire = 44cm$

$\textsf{let the radius of the circle be }r \rm \: cm$

$\rm \: then \: 2 \pi \: r = 44 \implies \: 2 \times \large \frac{22}{7} \small r = 44 \implies \: r = 7$

$\rm \therefore \: area \: of \: the \: circle = \pi \: r {}^{2}$

$\large \rm \: = \huge( \small \frac{22}{7} \times 7 \times 7 \huge) \small \:cm {}^{2} = 154 \: cm {}^{2}$