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 circ

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.

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2 months 2021-12-03T09:07:46+00:00 2 Answers 0 views 0

The area of the circle is 616 cm²

Step-by-step explanation:

Area of square = side × side

Side² = 484

⇒ Side² = ⇒ 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

2.        So, perimeter of the square is 88cm

__________________________

✒2πr= 88   So radius of the circle is 14

__________________________

Now

✒Area of circle =   So, Area of circle is 616cm^2