To find the length of the arc in a circle, you can use the formula:
\[ \text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r \]
where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.
In your case, the central angle \(\theta\) is \(45^\circ\), and the radius \(r\) is given as \(14 , \text{cm}\).
Now, plug in the values:
\[ \text{Arc Length} = \frac{45}{360} \times 2\pi \times 14 \]
First, simplify \(\frac{45}{360}\):
\[ \frac{45}{360} = \frac{1}{8} \]
Now, calculate the arc length:
\[ \text{Arc Length} = \frac{1}{8} \times 2\pi \times 14 \]
\[ = \frac{1}{8} \times 28\pi \]
\[ = \frac{28\pi}{8} = \frac{7\pi}{2} \]
Now, you can calculate this value approximately by using \(\pi \approx 3.14\):
\[ \text{Arc Length} \approx \frac{7 \times 3.14}{2} \approx \frac{21.98}{2} \approx 10.99 , \text{cm} \]
Thus, the length of the arc is approximately \(10.99 , \text{cm}\). If you want the exact answer in terms of \(\pi\):
\[ \text{Arc Length} = \frac{7\pi}{2} , \text{cm} \]