To find the area of a sector of a circle, you can use the formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle in degrees,
- \( r \) is the radius of the circle.
Given:
- \( r = 16 \) cm
- \( \theta = 72 \) degrees
Now, apply the values to the formula:
\[ A = \frac{72}{360} \times \pi \times (16)^2 \]
First, calculate \( (16)^2 \):
\[ (16)^2 = 256 \]
Now, substitute it into the area formula:
\[ A = \frac{72}{360} \times \pi \times 256 \]
Simplifying \( \frac{72}{360} \):
\[ \frac{72}{360} = \frac{1}{5} \quad (\text{since } 72 \div 72 = 1 \text{ and } 360 \div 72 = 5) \]
So now we have:
\[ A = \frac{1}{5} \times \pi \times 256 \]
This can be calculated as:
\[ A = \frac{256\pi}{5} = 51.2\pi \text{ cm}^2 \]
Thus, the area of the sector is:
\[ \boxed{51.2\pi \text{ cm}^2} \]