A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of `60^(@)` at its centre. Find the radius of the circle. `["Use" pi = (22)/(7)]`

Answer

To solve the problem step by step, we will follow the mathematical approach outlined in the video transcript.

### Step-by-Step Solution

1. **Identify the Given Information:**
- Length of the wire (arc length) = 22 cm
- Central angle (θ) = 60 degrees
- We will use π = 22/7.

2. **Convert the Angle from Degrees to Radians:**
- We know that \( 180^\circ \) is equivalent to \( \pi \) radians.
- To convert \( 60^\circ \) to radians, we can use the conversion factor:
\[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \]
- Thus,
\[ 60^\circ = 60 \times \frac{\pi}{180} = \frac{\pi}{3} \text{ radians} \]

3. **Use the Formula for Arc Length:**
- The formula for the length of an arc (L) is given by:
\[ L = r \times \theta \]
- Here, \( L = 22 \) cm and \( \theta = \frac{\pi}{3} \).

4. **Substitute the Values into the Formula:**
- We can rearrange the formula to solve for the radius (r):
\[ r = \frac{L}{\theta} \]
- Substituting the known values:
\[ r = \frac{22}{\frac{\pi}{3}} = 22 \times \frac{3}{\pi} \]

5. **Substitute the Value of π:**
- Now, substituting \( \pi = \frac{22}{7} \):
\[ r = 22 \times \frac{3}{\frac{22}{7}} = 22 \times \frac{3 \times 7}{22} \]

6. **Simplify the Expression:**
- The \( 22 \) in the numerator and denominator cancels out:
\[ r = 3 \times 7 = 21 \text{ cm} \]

### Final Answer:
The radius of the circle is **21 cm**.