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
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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