Question

A wire in the shape of a square of side 11m is rebent into shape ofa circle.Find the area of the circle​

Answer 1

✰ Solution :

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☞︎︎︎ Given :

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• side of square = 11m

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• Perimeter of square = Perimeter of circle

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☞︎︎︎ Perimeter = 4 × side

➪ P = 4 × 11m

∴ Perimeter = 44m

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• Now,

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➪ Perimeter of square = Circumference of circle

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☞︎︎︎ Circumference of circle = 2πr

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$\large \implies \rm \:44 = 2 \times \dfrac{22}{7} \times r$

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$\large \implies \rm \:44 = \dfrac{44}{7} \times r$

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• On Transposing The Terms :

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$\large \mapsto \rm \: 44 \times \dfrac{7}{44} = radius \\ \\ \\ \large \mapsto \rm \: \cancel{44} \times \dfrac{7}{ \cancel{44}} = radius$

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∴ Radius of circle = 7m

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• Finding Area Of Circle :

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☞︎︎︎ Area = πr²

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$\large \implies \rm \:area = \dfrac{22}{7} \times 7 \times 7 \\ \\ \\ \large \implies \rm \:area = \dfrac{22}{ \cancel7} \times \cancel 7 \times 7$

$\large \implies \rm \: area = 22 \times 7$

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$\boxed{ \boxed{\large \therefore \: \rm{area = 154 {m}^{2} }}}$