Calculate the length of the arc of a circle of radius 31.0 cm which subtands and angle of `(pi)/(6)` at the centre.

Options

A. 11.7 cm
B. 14.7 cm
C. 16.7 cm
D. 15.7 cm

Explanation

To calculate the length of the arc of a circle given the radius and the angle subtended at the center, we can use the formula for arc length:

\[ L = r \theta \]

where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Radius \( r = 31.0 \, \text{cm} \)
- Angle \( \theta = \frac{\pi}{6} \, \text{radians} \)

2. **Substitute the Values into the Formula**:
\[ L = r \theta = 31.0 \times \frac{\pi}{6} \]

3. **Calculate the Arc Length**:
- First, calculate \( \frac{\pi}{6} \):
\[ \frac{\pi}{6} \approx 0.5236 \, \text{(using } \pi \approx 3.14\text{)} \]
- Now, multiply:
\[ L = 31.0 \times 0.5236 \approx 16.23 \, \text{cm} \]

4. **Final Result**:
The length of the arc is approximately \( 16.23 \, \text{cm} \).