A

Step 1: Understand that the area of a circle is given by the formula:
$$A = \pi r^2$$ where A is the area and r is the radius.
Step 2: Differentiate the area with respect to time (t) to find the rate of change of area:
$$\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$$
Step 3: Given that the radius r is 8 cm and the speed of the waves or the rate of increase of the radius is $$\frac{dr}{dt} = 5 \text{ cm/s}$$, we can substitute these values into the differentiated equation:
$$\frac{dA}{dt} = 2\pi (8) (5)$$
Step 4: Calculate the expression:
$$\frac{dA}{dt} = 80\pi\text{ cm}^2/s$$
Step 5: Approximating for practical purpose, using $$\pi \approx 3.14$$:
$$\frac{dA}{dt} \approx 80 \times 3.14 = 251.2 \text{ cm}^2/s$$
Therefore, the enclosed area is increasing at approximately 251.2 cm²/s.