A stone is dropped into a pand. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of 2 inch/sec. How fast will the area of the wave increase ?
(a) when the radius is 5 inch?
(b) after 5 seconds ?

Explanation

To solve the problem, we need to find how fast the area of the wave increases as the radius of the outermost ripple increases. We will use the formula for the area of a circle and apply related rates.

### Step-by-Step Solution:

1. **Understand the Problem**:
- The radius \( r \) of the circle is increasing at a rate of \( \frac{dr}{dt} = 2 \) inches/second.
- We need to find \( \frac{dA}{dt} \), the rate of change of the area of the circle.

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