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 of the sector in degrees,
- \( r \) is the radius of the circle.
Given:
- \( r = 16 \) cm,
- \( \theta = 72^\circ \).
Now, we substitute the values into the formula:
\[ A = \frac{72}{360} \times \pi (16)^2 \]
First, calculate \( (16)^2 \):
\[ (16)^2 = 256 \]
Then substitute this back into the area formula:
\[ A = \frac{72}{360} \times \pi \times 256 \]
Now, simplify \( \frac{72}{360} \):
\[ \frac{72}{360} = \frac{1}{5} \quad \text{(since 72/72 = 1 and 360/72 = 5)} \]
Now we have:
\[ A = \frac{1}{5} \times \pi \times 256 \]
Calculating that:
\[ A = \frac{256\pi}{5} \]
Now, perform the calculation:
\[ \frac{256}{5} = 51.2 \]
So, the area of the sector is:
\[ A = 51.2\pi , \text{cm}^2 \]
Thus, the correct answer is:
A=51.2π cm²