Find the length of an arc of a circle of radius 10 cm which subtends an angle of `45^(@)` at the center

Answer

To find the length of an arc of a circle with a radius of 10 cm that subtends an angle of 45 degrees at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius \( R = 10 \) cm
- Angle \( \theta = 45^\circ \)

2. **Convert the angle from degrees to radians**:
- The formula to convert degrees to radians is:
\[ \text{radians} = \theta \times \frac{\pi}{180} \]
- For \( 45^\circ \):
\[ \theta = 45 \times \frac{\pi}{180} = \frac{\pi}{4} \text{ radians} \]

3. **Use the formula for the length of an arc**:
- The formula for the length of an arc \( L \) is given by:
\[ L = R \times \theta \]
- Substitute the values of \( R \) and \( \theta \):
\[ L = 10 \times \frac{\pi}{4} \]

4. **Calculate the length of the arc**:
- Simplifying the expression:
\[ L = \frac{10\pi}{4} = \frac{5\pi}{2} \]
- To get a numerical value, we can approximate \( \pi \approx 3.14 \):
\[ L \approx \frac{5 \times 3.14}{2} = \frac{15.7}{2} = 7.85 \text{ cm} \]

5. **Final answer**:
- The length of the arc is approximately \( 7.85 \) cm.