Question : When a wire is bent in the form of a square, then the area enclosed by it is 5929 cm2. If the wire is bent into the form of a circle, then what will be the area enclosed by the wire?
Option 1: 7546 cm2
Option 2: 8542 cm2
Option 3: 7632 cm2
Option 4: 6954 cm2
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Correct Answer: 7546 cm 2
Solution : Given: When a wire is bent in the form of a square, then the area enclosed by it is 5929 cm 2 . Let the sides of the square be $a$. Then, $a^2=5929$ ⇒ $a=77$ cm Now, the length of the wire = perimeter of the square = 4$a$ = 4 × 77 = 308 cm So, the circumference of the circle = 308 cm Let the radius of the circle be $r$. So, $2\pi r=308$ ⇒ $r=308×\frac{7}{22}×\frac{1}{2}$ ⇒ $r=49$ So, the area of the circle $= \pi r^2 = \frac{22}{7}×49×49$ = 7546 cm 2 Hence, the correct answer is 7546 cm 2 .
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