A wire is bent in the form of a square of side 16.5 cm . It is straightened and then bent into a circle. What is the radius of the circle so formed ? (Take `pi=(22)/(7))`

Options

A. 16.5 cm
B. 11.5 cm
C. 10.5 cm
D. 12.5 cm

Answer

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

### Step 1: Calculate the perimeter of the square.
The perimeter (P) of a square can be calculated using the formula:
\[ P = 4 \times \text{side} \]
Given that the side of the square is 16.5 cm, we can substitute this value into the formula:
\[ P = 4 \times 16.5 \]
\[ P = 66 \text{ cm} \]

### Step 2: Understand that the perimeter of the square is equal to the circumference of the circle.
When the wire is straightened and bent into a circle, the length of the wire remains the same. Therefore, the perimeter of the square (66 cm) is equal to the circumference (C) of the circle:
\[ C = 66 \text{ cm} \]

### Step 3: Use the circumference formula to find the radius of the circle.
The formula for the circumference of a circle is:
\[ C = 2 \pi r \]
Where \( r \) is the radius of the circle. We can set the circumference equal to the length of the wire:
\[ 66 = 2 \pi r \]

### Step 4: Solve for the radius \( r \).
To find \( r \), we rearrange the equation:
\[ r = \frac{66}{2 \pi} \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ r = \frac{66}{2 \times \frac{22}{7}} \]
\[ r = \frac{66 \times 7}{2 \times 22} \]
\[ r = \frac{462}{44} \]
Now, simplify \( \frac{462}{44} \):
\[ r = \frac{231}{22} \]
Calculating \( \frac{231}{22} \):
\[ r = 10.5 \text{ cm} \]

### Final Answer:
The radius of the circle formed is \( 10.5 \text{ cm} \).

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