Question

A steel wire when bent in the form of a square encloses an area of 484cm² . The same wire is bent in the form of a circle . Find the area of the circle ?​

Answer 1

Given:–

• A steel wire when bent in the form of a square encloses an area of sq.cm . The same wire is bent in the form of a circle .

To Find:–

• Area of the Circle

Formulas Used:–

• Area of a square = (side)² sq.cm
• Circumference if a circle = $\sf\pi r ^{2}$ units
• Area of a circle = $\sf\pi r ^{2}$

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Required Solution:–

Area of a square (steel wire) = 482sq.cm

⠀➟⠀⠀⠀⠀⠀⠀⠀⠀⠀(side)²⠀= (22)² sq.cm

⠀➟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀side⠀= 22 cm.

Hence, Perimeter of the square wire = (22 × 4) cm = 88 cm

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Now, Circumference of the circle = 88 cm

➟⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf2\pi r ^{2}$= 88

$\sf \: ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \times \dfrac{22}{7} \times r = 88 \\ ➟ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: r = \frac{88 \times 7}{44} = 14 \: m$

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Area of circle = $\sf\pi r ^{2}$

⠀⠀⠀⠀⠀⠀= $\sf \:\dfrac{22}{7}\times 14 \times 14 = 616 \: sq.cm$

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• Hence, Area of circle is 616 sq.cm