Question

A steel wire when bent in the form of square encloses an area of 121cm². If the same wire is bent in the form of a circle, find the area of the circle.

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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