Question

A steel wire when bent inthe form of a square encloses an area of 121 sq cm yhe same wire is bent in them form a circle find the area of circle

Answer 1

Area of a square=a^2
or 121=a^2
.•.a=√121
=11cm
now, perimeter of square=4a
=4×11
=44cm
now, perimeter of square=perimeter of circle
or 44=2πr
or r=44×7/2×22
or r=7 cm

so, Area of circle=πr^2
=22×7×7/7
=154 cm^2 answer

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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