If piece of wire 20 cm long is bent into the form of an are of a circle subending an angle of `60^@` at its centre. The radius of the circle is:

Options

A. `60/picm`
B. `20/picm`
C. `30/picm`
D. `15/picm`

Answer

To find the radius of the circle formed by bending a 20 cm long piece of wire into an arc that subtends an angle of 60 degrees at the center, we can use the formula for the length of an arc.

### Step-by-Step Solution:

1. **Understand the formula for the length of an arc**:
The length of an arc (L) of a circle can be calculated using the formula:
\[ L = \frac{\theta}{360} \times 2\pi r \]
where \( \theta \) is the angle in degrees and \( r \) is the radius of the circle.

2. **Substitute the known values**:
Here, the length of the wire (which is the length of the arc) is 20 cm, and the angle \( \theta \) is 60 degrees. We can substitute these values into the formula:
\[ 20 = \frac{60}{360} \times 2\pi r \]

3. **Simplify the equation**:
First, simplify \( \frac{60}{360} \):
\[ \frac{60}{360} = \frac{1}{6} \]
So the equation becomes:
\[ 20 = \frac{1}{6} \times 2\pi r \]

4. **Multiply both sides by 6**:
To eliminate the fraction, multiply both sides by 6:
\[ 20 \times 6 = 2\pi r \]
This simplifies to:
\[ 120 = 2\pi r \]

5. **Divide both sides by \( 2\pi \)**:
To solve for \( r \), divide both sides by \( 2\pi \):
\[ r = \frac{120}{2\pi} \]
Simplifying this gives:
\[ r = \frac{60}{\pi} \]

6. **Calculate the value of \( r \)**:
Using \( \pi \approx 3.14 \):
\[ r \approx \frac{60}{3.14} \approx 19.1 \text{ cm} \]

### Final Answer:
The radius of the circle is approximately \( 19.1 \) cm.