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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