A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

Explanation

To solve the problem step by step, we will follow the process of applying derivatives to find the rate at which the area of the circular wave is increasing.

### Step 1: Understand the problem
We have a circular wave expanding in a lake after a stone is dropped. The radius of the wave increases at a constant speed of 5 cm/s. We need to find how fast the area of the circle is increasing when the radius is 8 cm.

### Step 2: Identify the formulas
The area \( A \) of a circle is given by the formula:
\[
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