Question

A steel wire , When Bent in the form of a square , enclose an area of 121 cm2. The same wire is bent in the form of a circle. Find the of the circle.


please do it fast.

Answer 1

Heya !!!


Area of square = 121 cm²





(Side)² = 121 cm²




Side = ✓121 = 11 cm



Perimeter of square = 4 × Side



=> 4 × 11


=> 44 cm


Therefore,





Circumference of the circle = Length of the wire = 44 cm




Length of wire = 44 cm



Let the radius of circle be R cm.



Then,


2πR = 44 cm


2 × 22/7 × R = 44 cm



R = ( 44 × 7 / 44 )


R = 7 cm


Therefore,




Area of circle = πR²


=> 22 /7 × 7 × 7



=> 154 cm².




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Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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