If area of circle increases at a rate of `2cm^(2)//sec` then find the rate at which area of the inscribed square increases.

Explanation

To solve the problem, we need to find the rate at which the area of the inscribed square increases when the area of the circle increases at a rate of \(2 \, \text{cm}^2/\text{sec}\).

### Step-by-Step Solution:

1. **Understanding the relationship between the circle and the inscribed square**:
- Let the radius of the circle be \( r \).
- The area \( A \) of the circle is given by the formula:
\[
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