A stone is dropped in a quiet lake. If the produced circular waves increase at a rate of 4 cm/sec, then find the rate of increase in its area when the redius of circular wave is 7 cm.

Explanation

To solve the problem step by step, we will use the formula for the area of a circle and apply the concept of derivatives.

### Step 1: Understand the problem
We need to find the rate of increase of the area of circular waves produced by a stone dropped in a lake, given that the radius of the waves increases at a rate of 4 cm/sec when the radius is 7 cm.

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