Question

The diagonal of a square is changing at the rate of \( 0.5 \, \text{cm/sec} \). Then the rate of change of area, when the area is 400 \( \text{cm}^2 \), is equal to:

• A. \( 20 \sqrt{2} \, \text{cm}^2/\text{sec} \)
• B. \( 10 \sqrt{2} \, \text{cm}^2/\text{sec} \)
• C. \( 1 \sqrt{2} \, \text{cm}^2/\text{sec} \)
• D. \( 5 \sqrt{2} \, \text{cm}^2/\text{sec} \)

Hint:

Use related rates to find the rate of change of area when the dimensions of a shape change.

Answer 1

The Correct Option is B

Step 1: Use related rates.
By using related rates, we find that the rate of change of area with respect to the diagonal is \( 10 \sqrt{2} \, \text{cm}^2/\text{sec} \).
Thus, the correct answer is (2).