A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is

Options

A. 22 cm
B. 14 cm
C. 11 cm
D. 7 cm

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the perimeter of the square
The perimeter (or total length of the wire) of a square can be calculated using the formula:
\[ \text{Perimeter} = 4 \times \text{side} \]
Given that the side of the square is 22 cm, we can calculate the perimeter as follows:
\[ \text{Perimeter} = 4 \times 22 \, \text{cm} = 88 \, \text{cm} \]

### Step 2: Set the perimeter equal to the circumference of the circle
When the wire is rebent to form a circle, the length of the wire remains the same. Therefore, the perimeter of the square is equal to the circumference of the circle. The formula for the circumference of a circle is:
\[ \text{Circumference} = 2 \pi r \]
Setting the perimeter of the square equal to the circumference of the circle, we have:
\[ 88 \, \text{cm} = 2 \pi r \]

### Step 3: Solve for the radius (r)
To find the radius, we need to isolate \( r \) in the equation:
\[ r = \frac{88 \, \text{cm}}{2 \pi} \]
Now, substituting \( \pi \) with \( \frac{22}{7} \) (a common approximation):
\[ r = \frac{88 \, \text{cm}}{2 \times \frac{22}{7}} = \frac{88 \, \text{cm} \times 7}{44} \]
Simplifying this gives:
\[ r = \frac{88 \times 7}{44} = \frac{616}{44} = 14 \, \text{cm} \]

### Conclusion
The radius of the circle formed by rebending the wire is:
\[ \boxed{14 \, \text{cm}} \]

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