Question : A copper wire is bent in the form of a square and it encloses an area of 30.25 cm2. If the same wire is bent to form a circle, then find the area of the circle. [Use $\pi=\frac{22}{7}$]
Option 1: 38.50 cm2
Option 2: 42.25 cm2
Option 3: 35 cm2
Option 4: 30.25 cm2
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Correct Answer: 38.50 cm 2
Solution : Given, the area of the square formed by copper wire = 30.25 cm 2 Area of square = s 2 where s is the side of the square. ⇒ 30.25 = s 2 ⇒ s = 5.5 cm Now, total length of wire = 4s = 4 × 5.5 = 22 cm Let $r$ be the radius of the circle. Length of copper wire = Perimeter of circle formed ⇒ 4s = 2$\pi r$ ⇒ 22 = $2(\frac{22}{7}) r$ ⇒ $r$ = 3.5 cm Area of required circle = $\pi r^2$ = $\frac{22}{7}\times 3.5\times 3.5$ = 38.50 cm 2 Hence, the correct answer is 38.50 cm 2 .
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