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The wire bent in the form of square encloses an area of 121 cm2. What is the enclosed area when same wire is bent in the form of circle?1. 154 cm22. 150 cm23. 44 cm24. 77 cm2 |
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Answer» Correct Answer - Option 1 : 154 cm2 Given: Area of wire bent in the form of square = 121 cm2 Concepts used: Area of square = (Side)2 The perimeter of wire bent in the form of square = Perimeter of wire bent in the form of the circle The perimeter of square = 4 × side of the square Perimeter/Circumference of circle = 2πr Area of circle = πr2 Where r → Radius Calculation: Area of square = (Side)2 ⇒ 121 cm2 = (Side)2 ⇒ Side = √121 cm ⇒ Side of square = 11 cm The perimeter of wire bent in the form of square = 4 × side of the square ⇒ 4 × 11 cm ⇒ 44 cm Let the radius of the circle be r cm. Perimeter of wire bent in the form of square = Perimeter of wire bent in the form of circle 44 cm = 2πr ⇒ 44 cm = 2 × (22/7) × r ⇒ (44 × 7)/44 cm = r ⇒ r = 7 cm Area of circle = πr2 ⇒ 22/7 × (7)2 cm2 ⇒ (22/7) × 49 cm2 ⇒ 154 cm2 ∴ The wire encloses an area of 154 cm2 when bent in the form of circle. |
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