A wire is bent in the form of a square of side 66 m . It is cut and again bent in the form of a circle. The diameter of this circle is :

Options

A. 42 m
B. 84 m
C. 21 m
D. none of these

Answer

To find the diameter of the circle formed by bending a wire that was initially shaped into a square, we can follow these steps:

### Step 1: Calculate the perimeter of the square
The perimeter \( P \) of a square is given by the formula:
\[ P = 4 \times \text{side} \]
Given that the side of the square is 66 m, we can substitute this value into the formula:
\[ P = 4 \times 66 = 264 \text{ m} \]

### Step 2: Set the perimeter of the square equal to the circumference of the circle
When the wire is bent into the shape of a circle, the length of the wire remains the same. Therefore, the perimeter of the square is equal to the circumference \( C \) of the circle:
\[ C = P = 264 \text{ m} \]

### Step 3: Use the circumference formula to find the radius
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
We can set this equal to the perimeter we calculated:
\[ 264 = 2 \pi r \]
To find the radius \( r \), we can rearrange the equation:
\[ r = \frac{264}{2 \pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{264}{2 \times \frac{22}{7}} = \frac{264 \times 7}{44} = \frac{1848}{44} = 42 \text{ m} \]

### Step 4: Calculate the diameter of the circle
The diameter \( d \) of a circle is twice the radius:
\[ d = 2r = 2 \times 42 = 84 \text{ m} \]

### Final Answer
The diameter of the circle is \( 84 \text{ m} \).

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