Question

A wire, when bent in the form of a square, encloses an area of 484 cm². If the same wire is bent to form a circle, find the area of the circle.
please answer with prosedure properly​

Answer 1

Answer:

The area of the circle is 616 cm²

Step-by-step explanation:

Area of square = side × side

Side² = 484

⇒ Side² = $\sqrt{484}$

⇒ Side = 22 cm

★ Find the perimeter of square

The perimeter of square = 4 × side

⇒ 4 × 22

⇒ 88 cm

Therefore,

Length of wire = 88 cm

Circumference of the circle = 2 π r

★Find the radius of the circle

Let,

The radius of the circle = r

So,

⇒ 2 π r = 88

⇒ 2 × 22 / 7 × r = 88

⇒ 44 / 7 × r = 88

⇒ 44 r = 88 × 7

⇒ 44r = 616

⇒ r = 616 / 44

⇒ r = 14

Now,

Find the area of circle

The area of circle = π r²

⇒ 22 / 7 × 14 × 14

⇒ 22 / 7 × 196

⇒ 4312 / 7

⇒ 616

Therefore,

The area of the circle is 616 cm²

Answer 2

${ \bf{ \underline{ \underline{ \red{Solution}}}}}$

${ \bf{Side \: of \: square \: = \sqrt{area}}}$

$= \sqrt{484}$

$= 22cm$

${ \bf{ We \: know \: that }}$

${ \bf{Perimeter \: of \: square = 4 \times side}}$

$= 4 \times 22$

${ \mathtt{ \pink{ \underline{ \underline{88}}}}}$

So, perimeter of the square is 88cm

__________________________

✒Radius of circle =2πr

✒2πr= 88

$2 \times \frac{22}{7} \times r = 88$

$r = \frac{616}{44}$

${ \mathtt{ \pink { \underline{ \underline{14}}}}}$

So radius of the circle is 14

__________________________

Now

✒Area of circle =

${ \bf{ Area \: of \: circle = π {r}^{2}}}$

$\frac{22}{7} \times {14}^{2}$

${ \mathtt{ \green{ \boxed{616}}}}$

So, Area of circle is 616cm^2

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