To find the area of a sector formed by a central angle in a circle, you can use the formula:
\[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \]
where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.
For your case:
- \(\theta = 60\) degrees,
- \(r = 4\) cm.
Plugging the values into the formula:
\[ \text{Area} = \frac{60}{360} \times \pi \times (4^2) \]
Calculating \(4^2\):
\[ 4^2 = 16 \]
Now substitute back into the area formula:
\[ \text{Area} = \frac{60}{360} \times \pi \times 16 \]
Simplifying \(\frac{60}{360}\):
\[ \frac{60}{360} = \frac{1}{6} \]
Now, we substitute this into the area expression:
\[ \text{Area} = \frac{1}{6} \times \pi \times 16 = \frac{16\pi}{6} = \frac{8\pi}{3} \]
Thus, the area of the sector is:
\[ \text{Area} \approx \frac{8 \times 3.14}{3} \approx \frac{25.12}{3} \approx 8.38 \text{ cm}^2 \]
So the exact area of the sector is \(\frac{8\pi}{3}\) cm², and approximately \(8.38\) cm².