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A blacksmith bent a steel wire, in the form of a square, encloses an area of 484 sq. cm. The same wire he bent in the form of a circle. Find the area of circle (In sq.cm).1. 5202. 5443. 6604. 616 |
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Answer» Correct Answer - Option 4 : 616 Given: Area of square = 484 sq. cm Square wire is converted into circle Formula used: Perimeter of circle = 2π r, where r = radius of circle Area of circle = π r2 Perimeter of square = 4a, where a = side of the square Concept used: When square shape bent into circle, perimeter of square becomes equal to perimeter of circle Area of square = a2 ∴ a = √area = √484 = 22 cm ∴ perimeter of square = 4a = 4 × 22 = 88 cm Now, perimeter of circle = perimeter of square = 88 cm ⇒ 2π r = 88 ∴ r = 88 / 2π = 88 × 7 / 22 × 1 / 2 = 14 cm ∴ Area of circle = π r2 = 22 / 7 × 142 = 22 / 7 × 196 = 616 sq.cm Therefore, area of circle = 616 sq.cm |
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