A wire is bent in the form of a circle of 56 cm radius. It is opened and bent to form a square. The side of the square will be:

Options

A. 16 cm
B. 44 cm
C. 56 cm
D. 88 cm

Answer

To solve the problem step by step, we will first find the circumference of the circle formed by the wire and then use that to determine the side length of the square formed from the same wire.

### Step-by-Step Solution:

**Step 1: Find the Circumference of the Circle**
- The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

- Given that the radius \( r = 56 \) cm, we can substitute this value into the formula:
\[ C = 2 \pi (56) \]

**Step 2: Calculate the Circumference**
- Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 56 \]
\[ C = \frac{44 \times 56}{7} \]
\[ C = \frac{2464}{7} \approx 352 \text{ cm} \]

**Step 3: Understand the Relationship Between the Wire and the Square**
- When the wire is bent to form a square, the length of the wire remains the same, which means the perimeter of the square is equal to the circumference of the circle.

**Step 4: Set Up the Equation for the Perimeter of the Square**
- The perimeter \( P \) of a square is given by:
\[ P = 4 \times \text{side} \]
- Since the perimeter of the square is equal to the circumference of the circle:
\[ 4 \times \text{side} = 352 \text{ cm} \]

**Step 5: Solve for the Side Length of the Square**
- To find the side length, we divide the perimeter by 4:
\[ \text{side} = \frac{352}{4} \]
\[ \text{side} = 88 \text{ cm} \]

### Final Answer:
The side of the square will be **88 cm**.

---