A wire in the form of a rectangle 18.7 cm long and 14.3 cm wide is reshaped and bent into the form of a circle. Find the radius of the circle so formed.

Answer

To find the radius of the circle formed by reshaping a wire in the form of a rectangle, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Perimeter of the Rectangle**:
The perimeter (P) of a rectangle can be calculated using the formula:
\[ P = 2 \times (l + b) \]
where \( l \) is the length and \( b \) is the breadth.

Given:
- Length \( l = 18.7 \, \text{cm} \)
- Breadth \( b = 14.3 \, \text{cm} \)

Substitute the values:
\[ P = 2 \times (18.7 + 14.3) = 2 \times 33 = 66 \, \text{cm} \]

2. **Relate the Perimeter of the Rectangle to the Circumference of the Circle**:
The perimeter of the rectangle is equal to the circumference (C) of the circle formed by the wire.
\[ C = 66 \, \text{cm} \]

3. **Use the Circumference Formula to Find the Radius**:
The circumference of a circle can be expressed as:
\[ C = 2 \pi r \]
where \( r \) is the radius and \( \pi \) can be approximated as \( \frac{22}{7} \).

Set the circumference equal to the calculated perimeter:
\[ 66 = 2 \times \frac{22}{7} \times r \]

4. **Solve for the Radius \( r \)**:
Rearranging the equation to isolate \( r \):
\[ r = \frac{66 \times 7}{2 \times 22} \]

Simplifying the right side:
\[ r = \frac{462}{44} = \frac{21}{2} = 10.5 \, \text{cm} \]

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

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