Question

a circular piece of thin wire is converted into a rhombus of side 11 cm find the diameter of a circular piece

Answer 1

I think it's the answer.

Answer 2

$\star\small\sf\underline\blue{Given:-}$

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• A circular piece of thin wire is converted into a rhombus of side 11 cm.

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$\star\small\sf\underline\blue{To\: Find:-}$

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• The diameter of the circular piece = ?

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$\star\small\sf\underline\blue{Solution:-}$

$\sf \: Let \: the \: radius \: of \: the \: circle \: be \: r \: cm.$

$\footnotesize\bold{\underline{\underline{\sf{\red{Therefore:-}}}}}$

$\: \sf \: Diameter = 2 \times radius \\\\ \sf \: Diameter = 2r \: cm \\ \\ \sf \: Circumference = 2\pi \: r$

$\footnotesize\bold{\underline{\underline{\sf{\red{Now:-}}}}}$

$\sf \: Each \: length \: of \: the \: side \: of \: the \: rhombus = 11 \: cm$

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$\star\small\sf\underline\blue{Therefore:-}$

$\sf \: Perimeter = 4 \times side \\ \\ \sf \: Perimeter = 4 \times 11 \: cm \\ \\ \sf \: Perimeter = 44 \: cm$

$\footnotesize\bold{\underline{\underline{\sf{\red{According\:to\: the\: problem:-}}}}}$

Circumference of the circle = Perimeter of the rombus

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$\leadsto \sf 2\pi \: r = 44 \\ \\ \leadsto \sf 2 \times \dfrac{22}{7} \times r = 44 \\ \\ \leadsto \sf \dfrac{44}{7} \times r = 44 \\ \\ \leadsto \sf \: r = \cancel{44} \times \dfrac{7}{ \cancel{44}} \\ \\ \leadsto \sf \: r = 7$

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$\star\small\sf\underline\blue{Therefore:-}$

$\sf \: Diameter = 2r \\ \\ \sf \: Diameter = 2 \times 7 \\ \\ \sf \: Diameter = 14 \: cm$

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$\star\small\sf\underline\blue{AnswEr:-}$

• The diameter of the circular piece is 14 cm.