Question

a silver wire when bent in the form of a square encloses an area of 484 square CM if the same wire is bent in the form of circle find the area of circle​

Answer 1

Given:

• A silver wire is bent to form square.
• Area of square formed = 484 cm²
• The same wire is bent into circle.

To find :

Area of circle

Formula used :

• Area of square = (side)²
• Perimeter of square = 4 × side
• Circumference of circle = 2πr
• Area of circle = πr²

Solution :

Firstly we need to find out side of square.

➝ (Side)² = 484 cm²

➝ Side = √(484 cm²)

➝ Side = ± 22 cm

As side can't be negative, therefore

➝ Side = 22 cm

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Now we will find length of wire.

➝ Length of silver wire = Perimeter of square formed

➝ Length of silver wire = 4 × side

➝ Length of silver wire = 4 × 22cm

➝ Length of silver wire = 88cm

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As the same wire is bent into circle,

Circumference of circle = Length of silver wire

➝ Circumference of circle = 88cm

➝ 2πr = 88cm

➝ 2×(22/7)×r = 88cm

➝ 44r/7 = 88cm

➝ 44r = 88×7 cm

➝ 44r = 616 cm

➝ r = 616 cm/44

➝ r = 14 cm

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Area of circle = πr²

➝ Area of circle = (22/7) × (14 cm) × (14 cm)

➝ Area of circle = 22 × 2cm × 14 cm

➝ Area of circle = 616 cm²

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ANSWER : 616 cm²

Answer 2

Given

• Area of square= 484cm²

To Find

• Area of Circle

Formula Used

• Area of square= (side)²
• Circumference of circle= 2πr
• Area of Circle= πr²
• Perimeter of square= 4× side

Solution

Area of square= (side)²

→Area of square= 484cm²

→484= (side)²

→side= √484

side= 22cm

Now The Square is bent into silver wire

then The length of silver wire be;

→ 22× 4

88cm

Length of silver wire= 88cm

Now the Silver wire is convert into Circle

• Therefore The length of silver wire will be the circumference of the circle.

Length of silver wire= Circumference of Circle

• Circumference of circle=88cm.

Circumference of circle= 2πr

88= 2×22/7 × r

r= 88×7/22×2

r= 616/44

r= 14 cm

• Radius of Circle be 14cm

Now ,

Area of circle = πr²

Area of circle = 22/7 × (14)²

Area of circle = 22/7 × 196

Area of circle = 22×28

Area of circle = 616 cm²

The Area Of Circle be 616cm²