Question

20. A circular piece of thin wire is converted into a rhombus of side 11 cm. Find the diameter of the circular piece
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Answer 1

$\large\bold\orange{\underline{Question:-}}$

✯ A circular piece of thin wire is converted into a rhombus of side 11 cm. Find the diameter of the circular piece.

$\large\bold\green{\underline{Answer:-}}$

✯ Perimeter of circle = Perimeter of rhombus

✯ 2πr = 4a

$\large\implies$ 2 × πr = 4 × 11

$\large\implies$ r = (4 × 11/ 2 × 22) × 7

$\large\implies$ r = 7 cm

Diameter = 2r

⠀⠀ ⠀⠀ ⠀= (2 × 7) cm

⠀⠀⠀⠀ ⠀ = $\boxed{\rm{\red{14 cm}}}$

Answer 2

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

To Find : Find the diameter of the circle piece ?

_______________

Solution : Let the area of rhombus be x cm.

$~$

$\dag ~\underline{\frak{\pmb{As ~we ~know ~that~:}}}$

• Perimeter of circle = Perimeter of rhombus
• $\boxed{\frak{\pmb{Circumference~of~circle~=~2πr}}}$★

$~$

$\dag ~\underline{\frak{\pmb{According~ to ~the~given~question~:}}}$

$~$

$\qquad{\sf:\implies{2πr~=~11~×~4}}$

$\qquad{\sf:\implies{2~×~\dfrac{22}{7}~×~r~=~44}}$

$\qquad{\sf:\implies{r~=~\dfrac{44~×~7}{2~×~22}}}$

$\qquad{\sf:\implies{r~=~\dfrac{44~×~7}{44}}}$

$\qquad{\sf:\implies{r~=~\cancel\dfrac{308}{44}}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{\pmb{r~=~7cm}}}}}}$★

$\qquad{\sf:\implies{d~=~2~×~r}}$

$\qquad{\sf:\implies{d~=~2~×~7}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{d~=~14cm}}}}}}$★

$~$

Hence,

• The diameter of circle piece is 14cm.