The radius of a circle is increasing uniformly at the rate of 4 cm/sec. Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Explanation

To solve the problem step by step, we follow these steps:

### Step 1: Understand the problem
We are given that the radius \( R \) of a circle is increasing at a rate of \( \frac{dR}{dt} = 4 \) cm/sec. We need to find the rate at which the area \( A \) of the circle is increasing when the radius is \( R = 8 \) 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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