Question

18) A wire is bent to form a square of
side 22 cm.If the wire is rebent to
form a circle, its radius is

1) 22 cm

2)14 cm

3)11 cm

4)7 cm​

Answer 1

Solution

• Firstly, considered the wire in shape of a square with side 22cm.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Finding\: its\: perimeter}}}$

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$\large{\boxed{\boxed{\sf{Perimeter_{(Square)} = 4 \times side}}}}$

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$\tt\longrightarrow{Perimeter = 4 \times 22}$

$\tt\longrightarrow{Perimeter = 88}$

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• As we can see that the same wire is bent to form a circle. Therefore, their perimeter are same.

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$\large{\boxed{\boxed{\sf{Circumference = 2 \pi r}}}}$

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Perimeter (Square) = Circumference

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$\tt\longmapsto{88 = 2 \times \dfrac{22}{7} \times r}$

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$\tt\longmapsto{44 = \dfrac{22}{7}r}$

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$\tt\longmapsto{r = \dfrac{44 \times 7}{22}}$

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$\tt\longmapsto{r = 2 \times 7}$

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$\tt\longmapsto{r = 14}$

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Hence,

• Radius of the circle is 14cm. Therefore, option (2) is correct.

Answer 2

Given:

↬A wire is bent to form a square of side 22cm

↬If the wire is rebent to form a circle.

To Find:

★it's radius.!

Solution:

we,know that the wire was first bent of form a square of side 22cm. and them bent to from a circle

$\tt\therefore \: perimeter \: of \: square = circumference \: of \: the \: circle$

↬Perimeter of square is 4 times it's side

$: \implies \sf \: perimeter = 4 \times 22 \\ \\ : \implies \sf \: perimeter = 88cm \: \:$

$\blue{ \underline{ \pink{ \mathfrak{ \:so \: circumference \: of \: the \: circle = 88cm}}}}$

$➺\sf \: formula \: to \: find \: circumference : \\ 2\pi \times \: radius$

_____________________

$: \implies \sf \: 2\pi \: r = 88cm \: \: \: \: \: \: \: \: \: \: \: \\ \\: \implies \sf 2 \times \frac{22}{7} \times r = 88cm \\ \\ : \implies \sf \frac{44}{7} \times r = 88cm \: \: \: \: \: \: \: \: \\ \\ : \implies \sf \frac{44r}{7} = 88cm \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \sf44r = 88 \times 7cm \: \: \: \: \: \\ \\ : \implies \sf44r = 616cm \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \sf \: r = \cancel \frac{616}{44} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \sf \: r = 14cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \underline{ \boxed{ \orange{ \mathfrak{ \therefore \: radius \: of \: the \: circle = 14cm}}}}}$

hope this helps.!!