Question

a copper wire when bent in the form of a square encloses an area of 121cmsquare.if the same wire is bent into the form of a circle.find the area of the circle

Answer 1

Area of square = 121cm²
S x S = 121
2S = 121
  S = √121
 S = 11

Perimeter of the square = 4 x S
                                          = 4 x 11
                                          = 44
Circumference of circle = 2$\pi$ r
                    44                =2 × 3.14 × r
                     44/2 × 3.14=r
              22 x 3.14=r
             69.28=r
Area = $\pi$ r²
         3.14 x 69.28²
         3.14 x 4799.7184
      
15071.115776

Hope it helps

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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