A copper wire is bent in the form of square with an area of `121 cm^2`. If the same wire is bent in the form of a circle, the radius (in cm) of the circle is (Take `pi = (22)/(7)`)

Options

A. 7
B. 10
C. 11
D. 14

Answer

To solve the problem step by step, we will find the radius of the circle formed by the same copper wire that was initially bent into a square.

### Step 1: Find the side length of the square
We know the area of the square is given as \(121 \, \text{cm}^2\). The formula for the area of a square is:
\[ \text{Area} = \text{side}^2 \]
Let the side length of the square be \(s\). Therefore, we can write:
\[ s^2 = 121 \]
To find \(s\), we take the square root of both sides:
\[ s = \sqrt{121} = 11 \, \text{cm} \]

### Step 2: Calculate the perimeter of the square
The perimeter \(P\) of a square is given by the formula:
\[ P = 4 \times \text{side} \]
Substituting the value of the side:
\[ P = 4 \times 11 = 44 \, \text{cm} \]

### Step 3: The length of the wire
Since the wire is bent in the shape of the square, the length of the wire is equal to the perimeter of the square:
\[ \text{Length of wire} = 44 \, \text{cm} \]

### Step 4: Find the radius of the circle
When the same wire is bent into the shape of a circle, the circumference \(C\) of the circle is equal to the length of the wire:
\[ C = 44 \, \text{cm} \]
The formula for the circumference of a circle is:
\[ C = 2\pi r \]
Where \(r\) is the radius. We can rearrange this to find \(r\):
\[ r = \frac{C}{2\pi} \]
Substituting the value of \(C\) and using \(\pi = \frac{22}{7}\):
\[ r = \frac{44}{2 \times \frac{22}{7}} = \frac{44 \times 7}{44} = 7 \, \text{cm} \]

### Final Answer
The radius of the circle is \(7 \, \text{cm}\).

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